US8977523B2 - Methods to estimate downhole drilling vibration amplitude from surface measurement - Google Patents

Methods to estimate downhole drilling vibration amplitude from surface measurement Download PDF

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US8977523B2
US8977523B2 US13/386,859 US201013386859A US8977523B2 US 8977523 B2 US8977523 B2 US 8977523B2 US 201013386859 A US201013386859 A US 201013386859A US 8977523 B2 US8977523 B2 US 8977523B2
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vibration
downhole
drilling
severity
tool assembly
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US20120130693A1 (en
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Mehmet Deniz Ertas
Jeffrey R. Bailey
Damian N. Burch
Lei Wang
Paul E. Pastusek
Shankar Sundararaman
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ExxonMobil Upstream Research Co
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    • E—FIXED CONSTRUCTIONS
    • E21—EARTH OR ROCK DRILLING; MINING
    • E21B—EARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
    • E21B45/00—Measuring the drilling time or rate of penetration
    • E—FIXED CONSTRUCTIONS
    • E21—EARTH OR ROCK DRILLING; MINING
    • E21B—EARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
    • E21B44/00—Automatic control systems specially adapted for drilling operations, i.e. self-operating systems which function to carry out or modify a drilling operation without intervention of a human operator, e.g. computer-controlled drilling systems; Systems specially adapted for monitoring a plurality of drilling variables or conditions
    • E—FIXED CONSTRUCTIONS
    • E21—EARTH OR ROCK DRILLING; MINING
    • E21B—EARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
    • E21B7/00—Special methods or apparatus for drilling
    • E21B7/28—Enlarging drilled holes, e.g. by counterboring
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B15/00—Systems controlled by a computer
    • G05B15/02—Systems controlled by a computer electric

Definitions

  • the present disclosure relates generally to the field of drilling operations, particularly to monitoring and optimizing the same using surface measurements and the estimation techniques taught herein. More particularly, the present disclosure relates to methods to estimate the effective vibration amplitudes of the bottom of the drill tool assembly, such as at or near a drill bit, based on evaluation of selected surface operating parameters.
  • Drill tool assembly vibrations are known to potentially have a significant effect on Rate of Penetration (ROP) and represent a significant challenge to interpret and mitigate in pursuit of reducing the time and cost of drilling subterranean wells.
  • Drill tool assemblies vibrate during drilling for various reasons related to one or more drilling parameters. For example, the rotary speed (RPM), weight on bit (WOB), mud viscosity, etc. each may affect the vibrational tendency of a given drill tool assembly during a drilling operation. Measured depth (MD), rock properties, hole conditions, and configuration of the drill tool assembly may also influence drilling vibrations.
  • drilling parameters include characteristics and/or features of both the drilling hardware (e.g., drill tool assembly) and the drilling operations.
  • drill tool assembly refers to assemblies of components used in drilling operations.
  • Exemplary components that may collectively or individually be considered a drill tool assembly include rock cutting devices, bits, mills, reamers, bottom hole assemblies, drill collars, drill strings, couplings, subs, stabilizers, MWD tools, motors, etc.
  • Exemplary rig systems may include the top drive, rig control systems, etc., and may form certain boundary conditions. Deployment of vibrationally poor drill tool assembly designs and conducting drilling operations at conditions of high downhole vibrations can result in loss of rate of penetration, shortened drill tool assembly life, increased number of trips, increased failure rate of downhole tools, and increased non-productive time. It is desirable to provide the drilling engineer and/or rig operating personnel with a useful but not overly complex tool utilizing readily available data and quickly estimating the vibrational tendencies of the drill tool assembly.
  • a fixed cutter bit often requires more torque than a corresponding roller cone bit drilling similar formations at comparable conditions, although both bits can experience torque issues. Increased bit torque can lead to an increase in the phenomenon known as “stick-slip,” an unsteady rotary speed at the bit, even when surface RPM remains substantially constant. Excessive stick-slip can be severely damaging to drill string assemblies. Roller cone bits may sometimes be more prone to axial vibration issues than corresponding fixed cutter bits. Although axial vibrations may be reduced by substituting fixed cutter bits for roller cone bits, some drilling operations with either type of bit may continue to experience axial vibration problems. Fixed cutter bits can be severely damaged by axial vibrations as the PDC wafer can be knocked off its substrate if the axial vibrations are severe.
  • Axial vibrations are known to be problematic for rotary tricone bits, as the classic trilobed bottomhole pattern generates axial motion at the bit.
  • MSE Manufacturing Specific Energy
  • US 2009/0250264 US 2009/0250264
  • MSE is particularly useful in identifying drilling inefficiencies arising from, for example, dull bits, poor weight transfer to the bit, and whirl. These dysfunctions tend to reduce ROP and increase expended mechanical power due to the parasitic torques generated, thereby increasing MSE.
  • the availability of real-time MSE monitoring for surveillance allows the driller to take corrective action.
  • One of the big advantages of MSE analysis is that it does not require real-time downhole tools that directly measure vibration severity, which are expensive and prone to malfunction in challenging drilling environments.
  • MSE analysis may not provide reliable information about the severity of torsional or axial oscillations.
  • Field data shows intervals for which MSE does detect such patterns and other instances for which there is no vibration signature in the MSE data. Therefore, it is desirable to have additional indicators complementary to MSE that can provide torsional and/or axial severity from surface data, thereby avoiding the costly step of deploying downhole tools just for this purpose.
  • DEA Project 29 was a multi-partner joint industry program initiated to develop modeling tools for analyzing drill tool assembly vibrations. The program focused on the development of an impedance-based, frequency-dependent, mass-spring-dashpot model using a transfer function methodology for modeling axial and torsional vibrations. These transfer functions describe the ratio of the surface state to the input condition at the bit.
  • the boundary conditions for axial vibrations consisted of a spring, a damper at the top of the drill tool assembly (to represent the rig) and a “simple” axial excitation at the bit (either a force or displacement).
  • U.S. Pat. No. 5,852,235 ('235 patent) and U.S. Pat. No. 6,363,780 ('780 patent) describe methods and systems for computing the behavior of a drill bit fastened to the end of a drill string.
  • '235 a method was proposed for estimating the instantaneous rotational speed of the bit at the well bottom in real-time, taking into account the measurements performed at the top of the drill string and a reduced model.
  • Rf a function of a principal oscillation frequency of a weight on hook WOH divided by an average instantaneous rotating speed at the surface of the drillstring
  • Rwob being a function of a standard deviation of a signal representing a weight on bit WOB estimated by the reduced physical model of the drill string from the measurement of the signal representing the weight on hook WOH, divided by an average weight on bit WOB 0 defined from a weight of the drill string and an average of the weight on hook WOH, and any dangerous longitudinal behavior of the drill bit determined from the values of Rf and Rwob” in real-time.
  • the tuned parameters of the model may drift away from values actually representing the vibrational state of the drilling assembly. This drift can result in inaccurate estimates of desired parameters.
  • the '031 reference fails to propose means to evaluate the quality of the torsional vibration estimate by comparison with downhole data, offers only simple means to calculate the downhole torsional vibrations using a basic torsional spring model, provides few means to evaluate the surface measurements, does not discuss monitoring surface measurements for bit axial vibration detection, and does not use the monitoring results to make a comprehensive assessment of the amount or severity of stick-slip observed for a selected drilling interval.
  • This reference merely teaches a basic estimate of the downhole instantaneous rotational speed of the bit for the purpose of providing an input to a surface drive control system. Such methods fail to enable real-time diagnostic evaluation and indication of downhole dysfunction.
  • the present disclosure relates to improved methods to estimate the effective vibration amplitudes of the bottom of the drill tool assembly, such as at or near a drill bit, based on evaluation of selected surface operating parameters.
  • the estimates may then be utilized, such as in advance of, during, or after drilling activities to enhance present or future drilling operations.
  • These methods and systems may be used to increase overall drilling performance by adopting corrective measures to mitigate excessive inefficiencies and operational dysfunctions associated with vibrational energies within the drilling assembly. Vibrations may include but are not limited to torsional, axial, and coupled torsional/axial vibrations.
  • Estimation of downhole vibrations from surface data can provide critical information to assess changes in operating parameters and bit selection.
  • stick-slip can vary during a drilling operation due to both formation changes and operating parameter variations, maintaining an estimation of the amount of stick-slip severity for the entire drilling interval can provide important information for a drilling operation. It is desirable to implement a usefully accurate, reliable, and dependable remote surveillance program based on surface data that is broadly applicable, easy to teach, and easy to implement, using various selected aspects of a wide variety of rig data logging equipment that is readily available to the individual drill teams.
  • the claimed subject matter includes a method to estimate severity of downhole vibration for a wellbore drill tool assembly, comprising the steps: a. Identifying a dataset comprising selected drill tool assembly parameters; b. Selecting a reference level of downhole vibration amplitude for the drill tool assembly; c. Identifying a surface drilling parameter and calculating a reference surface vibration attribute for the selected reference level of downhole vibration amplitude; d. Determining a surface parameter vibration attribute derived from at least one surface measurement or observation obtained in a drilling operation, the determined surface parameter vibration attribute corresponding to the identified surface drilling parameter (step c); and e.
  • the term drilling operation is defined broadly to include boring, milling, reaming or otherwise excavating material to enlarge, open, and/or create a wellbore, whether original drilling operation, planning a drilling operation, work-over operation, remedial operation, mining operation, or post-drilling analysis.
  • the claimed technology includes a. identifying a dataset comprising (i) parameters for a selected drill tool assembly comprising a drill bit, (ii) selected wellbore dimensions, and (iii) selected measured depth (MD); b. Selecting a reference value of downhole vibration amplitude for at least one of downhole torque, downhole weight on bit, downhole bit RPM, and downhole axial acceleration; c. Identifying a corresponding selected surface drilling parameter including at least one of surface torque, a surface hook-load, surface drill string rotation rate, and surface axial acceleration, and calculating a corresponding reference surface attribute value for the selected reference value of downhole vibration amplitude; d.
  • step c Determining a surface parameter vibration attribute value obtained in a drilling operation, the determined surface parameter vibration attribute value corresponding to the identified selected surface drilling parameter (step c); and e. Estimating a downhole vibration severity by evaluating the determined surface parameter vibration attribute value (step d) with respect to the identified reference surface vibration attribute value (step c).
  • the claimed improvements include a method to estimate severity of downhole vibration for a drill tool assembly, comprising the steps: a. Identifying a dataset comprising selected drill tool assembly parameters; b. Selecting a reference level of downhole vibration amplitude for the drill tool assembly; and c. Identifying one or more ratios of: the selected reference level of downhole vibration amplitude for the drill tool assembly (step b) to a calculated reference surface vibration amplitude; d. Determining a surface parameter vibration attribute derived from at least one surface measurement or observation obtained in a drilling operation, the determined surface parameter vibration attribute corresponding to the identified surface drilling parameter (step c); and e. Estimating the downhole vibration severity indicator by evaluating the determined surface parameter vibration attribute (step d) with respect to one or more of the identified ratios (step c).
  • the methods above may include a step to estimate the quality of the vibration severity estimate determined from surface data by comparison with downhole measured data, either during or after the drilling process.
  • the methods above may include a step to evaluate the vibration severity estimates from at least two drilling intervals for the purpose of a drilling performance assessment to recommend selection of a drilling parameter for a subsequent interval, which may include selection of one or more bit features or characteristics, or a change in the specified WOB or rotary speed, or both.
  • the methods above may include the use of vibration severity estimates from surface data to evaluate drilling performance for an interval to adjust at least one drilling parameter to maintain a vibration severity estimate value at a desired value or below a maximum value not to be exceeded during the operation.
  • FIG. 1 demonstrates a schematic view of a well showing a generalized environment in which the present systems and methods may be implemented.
  • FIG. 2 illustrates a simplified, exemplary computer system in which methods of the present disclosure may be implemented.
  • FIG. 3 illustrates an exemplary flow chart demonstrating an exemplary method for performing some aspects of the inventive subject matter.
  • FIG. 4 provides an exemplary scheme for computing a Torsional Severity Estimate (TSE) based on a cross-compliance at a period P 1 .
  • TSE Torsional Severity Estimate
  • FIG. 5 provides an exemplary scheme for computing a Torsional Severity Estimate (TSE) based on a primary period P 1 .
  • TSE Torsional Severity Estimate
  • FIG. 6 demonstrates an exemplary reference surface dTorque as a function of measured depth.
  • FIG. 7 demonstrates an exemplary fundamental Stick-Slip Period P 1 as a function of measured depth.
  • FIG. 8 provides an illustration of exemplary data whereby the surface operation parameter is Torque and the peak-to-peak surface parameter is dTorque.
  • FIG. 9 illustrates a method for estimating dTorque using downward crossing of the surface torque with its moving average.
  • FIG. 10A provides an illustration of an exemplary surface torque signal.
  • FIG. 10B shows the oscillatory part of the signal from FIG. 10A .
  • FIG. 10C provides a graphical estimate of the dominant vibrational period from the signal of 10 B computed using Fourier analysis.
  • FIG. 11 illustrates a surface dTorque—surface dRPM cross plot.
  • FIG. 12 demonstrates an exemplary combined torsional (TSE) stick-slip whirl interaction, illustrated using an MSE-TSE severity cross-plot.
  • TSE combined torsional
  • FIG. 13 exemplifies a combined analysis of MSE-TSE with respect to a Performance Metric.
  • FIG. 14 provides an illustration of an exemplary downhole and surface torsional severity demonstration.
  • FIG. 15 provides an exemplary illustration of measured dTorque and reference dTorque.
  • FIG. 16 is an exemplary illustration of measured and estimated torsional severity and quality factor.
  • FIG. 17 demonstrates an exemplary histogram of measured torsional severity from downhole data.
  • FIG. 18 illustrates an exemplary torsional severity estimate calculated from surface data using a nonlinear drill string model and the corresponding quality factor histogram.
  • FIG. 19 illustrates an exemplary torsional severity estimate calculated from surface data using a simple linear compliance model and the corresponding quality factor histogram.
  • FIG. 20 illustrates exemplary torsional severity estimates from surface data from two wells, using a selected drill string model.
  • FIG. 21 illustrates an exemplary discrete classification scheme for downhole vibration amplitude.
  • FIG. 1 illustrates a side view of a relatively generic drilling operation at a drill site 100 .
  • FIG. 1 is provided primarily to illustrate a drill site having a drilling rig 102 disposed above a well 104 drilled into a formation 110 .
  • the drilling rig 102 includes a drill tool assembly 106 including a drill bit 108 disposed at the end thereof.
  • the apparatus illustrated in FIG. 1 is illustrated in almost schematic form merely to present the representative nature thereof.
  • the present systems and methods may be used in connection with any currently available drilling equipment and is expected to be usable with any future developed drilling equipment. Similarly, the present systems and methods are not limited to land based drilling sites but may be used in connection with offshore, deepwater, arctic, and the other various environments in which drilling operations are conducted.
  • While the present systems and methods may be used in connection with any rotary drilling, milling, under-reaming, or boring operation, they are expected to be used primarily in wellbore drilling operations related to the recovery of hydrocarbons, such as for oil and gas wells.
  • References herein to drilling operations are to be understood expansively. Operators are able to remove rock, other formation, casing components, cement, and/or related materials using a variety of apparatus and methods, some of which are different from conventional forward drilling into virgin formation. Accordingly, the discussion herein referring to drilling parameters, drilling performance measurements, drilling vibrations, drilling vibration severity, drilling vibration amplitude, etc., refers to parameters, measurements, performance, vibrations, and severity during any of the variety of operations that are associated with a wellbore rotary drilling process.
  • drilling conditions will be used to refer generally to the conditions in the wellbore during the drilling operation.
  • the drilling conditions are comprised of a variety of drilling parameters, some of which relate to the environment of the wellbore and/or formation and others that relate to the drilling activity itself.
  • drilling parameters may include but are not limited to, any of rate of rotation (RPM), weight on bit (WOB), measured depth (MD), hole angle, hole diameter, characteristics of the drill bit and drill string, mud weight, mud flow rate, mud viscosity, rock properties, lithology of the formation, pore pressure of the formation, torque, pressure, temperature, rate of penetration, mechanical specific energy, etc., and/or combinations thereof.
  • RPM rate of rotation
  • WOB weight on bit
  • MD measured depth
  • Common attributes include mean value, standard deviation, root-mean-square, and other statistical values. Additional attributes of the parameters may include dominant period, dominant frequency, time rate of change, peak time rate of change (“slew rate”), peak-to-peak amplitude, moving average, spectral periodogram from Fourier analysis, and the like.
  • the present inventions and claimed subject matter provide methods for reliably and conveniently estimating various downhole vibration parameters from relatively available surface data, such estimations being useful to timely reduce unacceptable vibrations and improve drilling operations.
  • the measurements and data acquisitions performed at the top of the drill tool assembly can be obtained by means of sensors or an instrumented sub situated close to the top of the drill tool assembly, or may be obtained at or near the drilling rig.
  • the drill bit 108 advances through the formation 110 at a rate known as the rate of penetration (ROP, 108 ), which is commonly calculated as the measured depth (MD) drilled over time.
  • ROP rate of penetration
  • MD measured depth
  • formation conditions are location dependent, drilling conditions necessarily change over time as the wellbore penetrates varying formations. Moreover, the drilling conditions may change in manners that dramatically reduce the efficiencies of the drilling operation and/or that create less desired operating conditions.
  • the presently claimed subject matter demonstrates improved methods of predicting, estimating, and detecting changes in drilling conditions and the response of different bits and cutting tools to these formations.
  • Bit selection is a key parameter that affects drilling efficiency and the art of bit design continues to advance with new bit features that may be difficult to evaluate for a specific drilling application without using the bit to drill at least a portion of a formation of commercial interest.
  • Means to evaluate the performance of such a drill test may include the propensity of the bit to generate drilling vibrations, including torsional stick-slip vibrations.
  • the claimed subject matter provides means to efficiently quantify with a reasonable degree of accuracy the downhole vibration severity, relying only on calculable parameters and surface data measurements, thus avoiding the delays, costs, and complexity of providing actual downhole measurements.
  • This invention discloses a method to estimate the severity of one or more of RPM and WOB fluctuations at the bottom of the drill tool assembly in real time during drilling operations, or optionally before or after drilling to aid in drilling assembly planning or analysis.
  • This severity estimate is computed based on a mechanical description of the drilling assembly and real-time operating parameters (including torque, RPM, WOH, WOB) and measured depth (MD) readings taken from one or more of a surface drilling rig recording system and an instrumented surface sub. Additional information such as the wellbore trajectory, drilling fluid density and plastic viscosity, and friction factors can refine this estimate but is not required.
  • the estimated severity level may be displayed to the driller or an engineer, in a manner similar to rig-determined and displayed MSE data, to assist in drilling surveillance and operational decisions.
  • the driller may be provided (directly or indirectly) portions of the information in the form of predetermined tables or plots (e.g., for direct read and/or interpolation) that in conjunction with the rig-measured data can allow estimation of stick-slip severity, torque fluctuations, and axial vibration severity by monitoring the surface torque, RPM, and hookload on the driller's screen or rig parameters.
  • the severity of a given type of vibrational dysfunction can be described by a dimensionless ratio that compares the amplitude of dynamic fluctuations in a drilling parameter to its average value.
  • stick-slip severity may be related to the ratio of dynamic RPM variations at the drill bit to the average RPM at the bit. Since there is rarely permanent torsional deformation of the drill string, the average RPM of the bit (downhole) is substantially equal to the average RPM of the drill string at the surface.
  • a single dominant (“active”) vibrational mode at a specific frequency may account for a dominant portion of the dynamic variation in the observed drilling parameter.
  • active dominant
  • the claimed subject matter includes a method to estimate severity of downhole vibration for a wellbore drill tool assembly, comprising the steps: a. Identifying a dataset comprising selected drill tool assembly parameters; b. Selecting a reference level of downhole vibration amplitude for the drill tool assembly; c. Identifying a surface drilling parameter and calculating a reference surface vibration attribute for the selected reference level of downhole vibration amplitude; d. Determining a surface parameter vibration attribute derived from at least one surface measurement or observation obtained in a drilling operation, the determined surface parameter vibration attribute corresponding to the identified surface drilling parameter (step c); and e.
  • the term drilling operation is defined broadly to include boring, milling, reaming or otherwise excavating material to enlarge, open, and/or create a wellbore, whether original drilling operation, planning a drilling operation, work-over operation, remedial operation, mining operation, or post-drilling analysis.
  • vibration relates to vibration of one or more components of the drill tool assembly and comprises one or more of torsional vibration, axial vibration, lateral vibration, coupled torsional and axial vibrations, and combinations thereof.
  • the step of “identifying a dataset” may comprise selecting, for example, one or more drill tool assembly design parameters, wellbore dimensions, measured depth (MD), projected drilling operation parameters, wellbore survey data, and wellbore fluid properties.
  • the “reference level of downhole vibration amplitude” may be selected as, for example, a function of one or more of downhole drill tool assembly rotational velocity, downhole axial velocity, downhole axial acceleration, downhole axial load, downhole torsional moment, and combinations thereof.
  • selecting a reference level of downhole vibration amplitude may comprise, for example, selecting a downhole condition for the drill tool assembly for which the rotary velocity is momentarily zero. Momentarily zero means that for at least some discernable increment of time the downhole rotary velocity (RPM) comes to a halt or is not greater than five percent of the average RPM.
  • RPM downhole rotary velocity
  • selecting a reference level of downhole vibration amplitude may include, for example, selecting a downhole condition where a weight on bit (WOB) parameter is momentarily zero.
  • selecting a reference level of downhole vibration amplitude may comprise selecting an undesirable downhole condition, such as for example full stick-slip of the bit, bit axial disengagement from the formation, or momentarily exceeding some design or operating limit anywhere along the drill tool assembly, such as the make-up or twist-off torque of a connection, a bucking limit, tensile or torsional strength of a component.
  • a corresponding surface parameter may be identified that is physically connected to the selected downhole vibration parameter of interest.
  • a reference surface parameter vibration attribute may be calculated for the corresponding reference level of the downhole vibration.
  • Determining a surface parameter vibration attribute may refer to calculating, estimating, or otherwise obtaining a quantity related to one or more measured values of a surface parameter.
  • the term “surface parameter” as used herein is defined broadly to refer to physical properties, manifestations of vibrational energy, and operating conditions observed or measured at the surface. Typical vibration attributes of interest include but are not limited to the period of vibration of surface torque, peak-to-peak amplitude of surface torque, root-mean-square value of surface hookload, etc. Additional examples of surface parameter vibration attributes are provided herein.
  • a downhole vibration severity indicator may be calculated from the determined surface vibration parameter attribute obtained from the measured data, in consideration of the calculated reference level of the surface parameter corresponding to the selected reference level of the downhole vibration.
  • WO 2009/155062 filed on Jun. 17, 2008, describes certain methodologies based upon a frequency domain model to design a drill tool assembly for use in a drilling operation, based on drilling operations parameters and drill tool assembly data, utilizing torsional and axial vibration indices that characterize an excitation response.
  • the models described therein and presented as one embodiment below may optionally be used in conjunction with the present invention to compute the frequency response of the drill tool assembly and specifically to compute the dominant periods of vibration, as well as ratios of vibration amplitudes of one or more surface and downhole parameters for such periods.
  • the vibration amplitudes may provide information on the characteristic dynamic oscillations in one or more operating parameters such as torque, hookload, RPM, WOB and acceleration over a specified period or periods of vibration.
  • the vibration amplitude may be obtained from the Fourier component of the drilling operating parameters obtained at a specific frequency, or, if a single vibrational mode is dominant (active), from the maximum and minimum values that are observed during an interval longer than but comparable to the period of oscillation.
  • a period of oscillation refers to the time required for completion of one cycle of dynamic variation. This period corresponds to the normal modes of vibration associated with the drill tool assembly.
  • Vibration amplitude may be determined by various methods that may be considered essentially equivalent for signals of interest with respect to accurately determining amplitude.
  • the field of random vibrations teaches several ways to estimate A(t), which may in general vary in time, from a set of measurements. After means to remove a slowly-varying, steady, or “DC,” component, the residual signal typically has zero mean. The crossings of the signal with the time axis, in either the up or down direction, has significance because these time values help to determine the period. For one such cycle, the extreme values can be determined, and these values can be used to determine one estimate of the amplitude A(t).
  • a sine wave could be fit to the data for one such period with the coefficient A(t) determined by a minimum error approach.
  • the standard deviation of the signal can be determined for some moving time window or interval, and using mathematical relationships one may estimate the amplitude A(t) from these values.
  • Fourier analysis is yet another way to calculate the amplitude of a sinusoidal signal. Therefore, the phrase “vibration amplitude” is used to refer to the strength A(t) of a time-varying signal that may be determined by these and other means that are known to those skilled in the art, including processes that use FIR and IIR filters, state observers, Kalman filters, derivatives, integrals, and the like.
  • vibration severity can be considered to be related to the ratio of the vibration amplitude to the mean signal strength.
  • vibration severity can be considered to be related to the ratio of the vibration amplitude to the mean signal strength.
  • the factor of 2 is absent.
  • 100% stick-slip or “full stick-slip,” to correspond to the condition wherein the sinusoidal oscillation of the bit about its mean rate of rotation is such that it momentarily has zero RPM, for which the amplitude of the vibration is equal to the mean rotary speed.
  • Max(x) 2A
  • Min(x) 0
  • Mean(x) A
  • S(x) 100%. It is recognized that other more severe stick-slip conditions may occur, and the pattern may not be purely sinusoidal. This example is provided as a reference condition and is not limiting. Additional definitions of vibration severity are within the scope of the claimed subject matter.
  • the ratios of such amplitudes at different positions along the drill tool assembly for a given vibrational mode can be robustly estimated simply from the eigenfunction of the mode (also referred to as the “mode shape”), even under varying drilling conditions.
  • the active mode and its mode shape it is possible to reliably estimate the vibrational amplitude of a parameter associated with downhole behavior from an observation or determination of a related parameter at another location, such as at the surface.
  • the main benefit of the method outlined and claimed subject matter in this disclosure is that it allows real-time computation of the torsional and axial severity along with suitable alarm levels that diagnose downhole conditions without access to downhole vibration data.
  • this invention complements the operator's ROP management process that uses the Mechanical Specific Energy (MSE) as a diagnostic surface measurement of downhole behavior.
  • MSE Mechanical Specific Energy
  • the vibration severity estimates presented herein are complementary to the MSE data. Estimates of downhole vibrations from surface data may be compared with downhole data measurements for use in an evaluation of the quality of the vibration severity estimate. The accuracy of the physical model and proper selection of drilling parameter data will both contribute to increasing quality of the vibration severity estimates.
  • vibration severity estimates for complete drilling intervals may be used in drilling performance assessment to aid in bit selection and drilling parameter selection for use in drilling a subsequent interval. It is therefore important to assess the quality of the vibration severity estimate, using downhole data measurements, so as to understand the accuracy of the dynamic model and to conduct any necessary calibrations of the model. After a model has been calibrated and the quality of the estimate is known, it can be used with greater confidence for making operational and design decisions.
  • vibration severity estimates may be obtained for a specific bit drilling a specific interval under certain drilling conditions. If the vibration severity estimate indicates that the bit is not operating close to stick-slip, then one could reasonably choose a more aggressive bit or one or more other more aggressive operational parameters for a subsequent run, or a combination thereof. However, if the data shows that the bit is routinely in full stick-slip, a reduction in bit tooth or cutter depth-of-cut may be warranted, or alternatively less aggressive operating parameters would be advised. Such results are likely to be formation specific and thus one could contemplate the need to conduct such surveillance on a nearly continuous basis. Since it is most desirable to drill as long an interval as possible with a single bit, one important value of the diagnostics is to provide information for choosing a bit and operating parameters that have optimized performance over the interval taken as a whole.
  • the inventive subject matter claimed herein separately investigates each of the zero and first order terms in a perturbation expansion.
  • the fluctuation amplitudes of drilling operating parameters such as torque, WOH, WOB, and RPM are derived as the first order components of a perturbation expansion of the equations of motion of the drilling assembly.
  • the zero-order terms determine the baseline solution.
  • Second and higher order terms are not necessary for the claimed methods but could be calculated if desired.
  • Using the fluctuation amplitudes provides a practical approach to calculation of the torsional and axial behavior at the bottom of the drill string.
  • our calculations do not compute a real-time value of the rotational speed of the bit; our model calculations are not required to be carried out in real-time; our methods can make use of spectral analysis, and details from specific frequency(ies) may then be used for further computation; and we have no need to over-sample the data if the period of the active mode is known.
  • One method provided herein includes a step of selecting a reference downhole amplitude or vibration severity for a torsional or axial state to be diagnosed.
  • reference downhole conditions include: (1) the state of “full stick-slip” in which the torsional rotation of the bit momentarily comes to a full stop and then accelerates to a peak rate of rotation of approximately twice the average rotary speed; (2) the state of “bit bounce” for which the applied axial force of the bit on the bottom of the borehole is momentarily zero, after which it may increase to a value considerably in excess of its average value; (3) an axial vibration state in which the bit is lifted off the bottom of the borehole a sufficient distance such that the cutting element clears the present bottomhole cutting pattern; (4) extreme values of stick-slip such that the instantaneous torque value is negative and rises to a sufficient level to backoff drill string connections, which will depend on the specific hole size and drill string connections in use.
  • the reference downhole condition may be expressed as a vibration amplitude or as a vibration amplitude ratio.
  • a vibration amplitude ratio For example, one may specify the RPM range or, alternatively, full stick-slip for which the ratio of the vibration amplitude (A(t) above) to the average rotary speed is 1, or 100% stick-slip. It follows that other natural reference downhole vibration conditions may be selected, but these are ones of present interest.
  • the amplitudes and severity of the corresponding reference levels of surface parameters are calculated using the drilling parameters and the physical model, which includes as much descriptive physics as may be necessary for an accurate modeling estimate.
  • the reference surface condition may be simply a reference vibration amplitude of a single surface parameter (such as torque), or it may be a complex relation between multiple surface parameters (such as torque and rotary speed) for more complicated surface boundary conditions.
  • the vibration amplitude of the surface parameter is determined from measured data at the surface from a drilling operation, using one or more of the several methods indicated above.
  • the “vibration amplitude ratio” is calculated as the measured surface parameter vibration amplitude, divided by the reference level of the surface parameter calculated from the model and the drilling parameters for the reference downhole vibration amplitude.
  • This vibration amplitude ratio is an estimate of the downhole vibration severity.
  • This method can be generalized to include more than one reference level and additional surface parameter attributes such as primary period and other measures of the effective vibration amplitude.
  • the reference downhole condition is full stick-slip, for which the vibration amplitude of the rotary speed is equal to the mean RPM.
  • the surface torque vibration amplitude may be calculated from the physical model for this downhole vibration reference condition.
  • the vibration amplitude of the surface torque is determined from the measured surface data.
  • the ratio of the measured surface torque vibration amplitude to the calculated reference level is the torsional severity estimate (TSE).
  • a post-drill analysis may be performed on a well for which downhole measurements were made while drilling. These measurements can be compared to the reference level of downhole vibration amplitude to obtain a measured downhole vibration severity. Then any of a number of algorithms from the field of pattern recognition (also known as machine learning, statistical learning, data mining, and artificial intelligence) may be employed to train a computer program to automatically classify the severity of the downhole vibrations given only the corresponding topside measured data. Such algorithms include, but are not limited to, linear and logistic regression, discriminant analysis, and classification and regression trees.
  • the trained algorithms may be employed to autonomously estimate downhole vibration severity in real-time while drilling new wells. Though such learning algorithms need only employ the drilling measurements, their classification performance is greatly improved by also using the results of the physical models described herein as a baseline during training.
  • the adjustment of the at least one drilling parameter may be based on this one or more vibration amplitude ratio(s) and/or on the determined or identified drilling parameter change.
  • the identified change may be displayed for an operator with or without the underlying vibration amplitude ratio or severity level used to determine the change.
  • the determined change may also be presented and the operator may act to adjust drilling conditions based solely on the displayed change.
  • an operator or other person in the field may consider both the vibration amplitude ratios and the identified drilling parameter change.
  • the computer system may be adapted to change the drilling parameter without user intervention, such as by adjusting WOB, WOH, rotary speed, pump rate, etc.
  • the manner of adjusting the drilling parameter may change.
  • the present methods and systems may be implemented in a manner to adjust one or more drilling parameters during a drilling operation, but not necessarily in substantially real-time.
  • the data may be evaluated in a post-drill performance evaluation review, with subsequent recommendations on drilling parameter change, including selection of a drill bit or bit characteristics and features, for use in the drilling of a subsequent interval.
  • a recent important innovation is the use of depth-of-cut (DOC) control features on PDC bits, which limit the amount of cutter penetration at higher bit weights.
  • the DOC feature thus limits the bit torque at high bit weight. Evaluation of bit performance and optimizing the selection of DOC features has thus become more complex, and additional tools such as the present invention are necessary to maximize drilling performance.
  • the inventive technology may also include a software program that graphically characterizes the vibrational performance of the drill tool assembly.
  • the software program will graphically characterize the vibrational performance or tendency of a single configuration design for one or more vibrational modes.
  • the methodologies implemented to graphically characterize the torsional and axial vibration performance incorporate a common framework with some differences.
  • the software program input consists of entering ranges for various drilling operations parameters, such as WOB, RPM, drilling fluid density and viscosity, and bit depth, as well as various drill tool assembly design parameters, such as pipe and component dimensions, mechanical properties, and the locations of drill tool assembly components, such as drill collars, stabilizers and drill pipe. It has been observed that the proper modeling of drill pipe tool joints affects certain modes of vibration, and model accuracy depends on including these periodic elements of greater wall thickness, weight, and stiffness in the drill string model.
  • the program may allow for developing and maintaining multiple drill tool assembly design configurations as a storage record of the vibration amplitude ratios obtained for alternative drill tool assembly design configurations.
  • bit parameters depend heavily on details of the bit geometry, bit condition (new vs. dull), depth-of-cut (DOC) features, bottom-hole hydraulics, rock properties, etc.
  • the model does not attempt to predict these parameters, which are measurable or known to a large degree during drilling operations, but uses them as inputs to analyze the response of the drill tool assembly to excitations caused by the bit action.
  • the model is sufficiently complete that advanced modeling features may be examined, such as coupling between axial and torsional vibrations at the bit, as well as complex surface impedance characteristics, for which both torque and rotary speed may have dynamic variations at the surface, for example. It may also be noted that the effects of some of these parameters increase with increasing string length, and therefore greater model accuracy is required to maintain the vibration severity estimate quality for increasing drill string length.
  • the data regarding drilling operations may include specific data regarding drilling operating conditions and/or may include drilling operations parameters, which are ranges of available conditions for one or more drilling operational variables, such as WOB, WOH, RPM, fluid density and viscosity, etc.
  • An operational variable is an operational element over which an operator has some control.
  • the methods and systems of the present disclosure may obtain input data, such as for use in the frequency-domain models, from a drilling plan.
  • drilling plan refers to the collection of data regarding the equipment and methods to be used in a drilling operation or in a particular stage of a drilling operation.
  • FIG. 2 illustrates an exemplary, simplified computer system 400 , in which methods of the present disclosure may be implemented.
  • the computer system 400 includes a system computer 410 , which may be implemented as any conventional personal computer or other computer-system configuration described above.
  • the system computer 410 is in communication with representative data storage devices 412 , 414 , and 416 , which may be external hard disk storage devices or any other suitable form of data storage, storing for example, programs, drilling data, and post-drill analysis results.
  • data storage devices 412 , 414 , and 416 are conventional hard disk drives and are implemented by way of a local area network or by remote access.
  • data storage devices 412 , 414 , and 416 are illustrated as separate devices, a single data storage device may be used to store any and all of the program instructions, measurement data, and results as desired.
  • the data to be input into the systems and methods are stored in data storage device 412 .
  • the system computer 410 may retrieve the appropriate data from the data storage device 412 to perform the operations and analyses described herein according to program instructions that correspond to the methods described herein.
  • the program instructions may be written in any suitable computer programming language or combination of languages, such as C++, Java, MATLABTM, and the like, and may be adapted to be run in combination with other software applications, such as commercial formation modeling or drilling modeling software.
  • the program instructions may be stored in a computer-readable memory, such as program data storage device 414 .
  • the memory medium storing the program instructions may be of any conventional type used for the storage of computer programs, including hard disk drives, floppy disks, CD-ROMs and other optical media, magnetic tape, and the like.
  • the program instructions and the input data can be stored on and processed by the system computer 410 , the results of the analyses and methods described herein are exported for use in mitigating vibrations.
  • the obtained drill tool assembly data and drilling operations parameters may exist in data form on the system computer.
  • the system computer utilizing the program instructions may utilize frequency-domain models to generate one or more vibration amplitude ratios.
  • the vibration amplitude ratios may be stored on any one or more data storage devices and/or may be exported or otherwise used to mitigate vibrations.
  • the vibration amplitude ratios may be used by an operator in determining design options, drill plan options, and/or drilling operations changes.
  • the vibration amplitude ratios may be utilized by the computer system, such as to identify combinations of drilling parameters that best mitigate vibrations under given circumstances.
  • the system computer 410 presents output onto graphics display 418 , or alternatively via printer 420 . Additionally or alternatively, the system computer 410 may store the results of the methods described above on data storage device 416 for later use and further analysis.
  • the keyboard 422 and the pointing device (e.g., a mouse, trackball, or the like) 424 may be provided with the system computer 410 to enable interactive operation.
  • a graphical or tabular format display of vibration amplitude ratios may require two, three, or more dimensions depending on the number of parameters that are varied for a given graphical or tabular representation.
  • the graphics or table printed 420 or displayed 418 is merely representative of the variety of displays and display systems capable of presenting three and four dimensional results for visualization.
  • the pointing device 424 and keyboard 422 is representative of the variety of user input devices that may be associated with the system computer.
  • the multitude of configurations available for computer systems capable of implementing the present methods precludes complete description of all practical configurations.
  • the multitude of data storage and data communication technologies available changes on a frequent basis precluding complete description thereof. It is sufficient to note here that numerous suitable arrangements of data storage, data processing, and data communication technologies may be selected for implementation of the present methods, all of which are within the scope of the present disclosure.
  • the present technology may include a software program that visually characterizes the vibrational performance of one or more drill tool assemblies using one or more of graphical and tabular formats.
  • the inventive methodology involves use of a “base model” to develop and/or calculate the baseline solution, the frequency eigenmodes, and the dynamic linear response functions for a given set of input parameters.
  • a “base model” is a dynamic perturbation model of the equations of motion for the drill tool assembly under given input drilling operations parameters and conditions.
  • the dynamic model comprises simply the first order terms in the dynamic variables. Higher order terms in the perturbation theory could be calculated but are not provided here.
  • the tractability and computational simplicity of the present methods are preserved through the use of a robust base model used to determine a baseline solution, or a baseline condition of the drill tool assembly in which no vibration is present.
  • Linear response functions are also developed based on the base model.
  • the linearization of the motion around the baseline solution allows independent linear harmonic analysis of the eigenstates at each vibration frequency and the use of superposition to analyze the overall dynamic motion.
  • the vibration-related factors may be incorporated into the frequency-domain models by way of one or more linear response functions, which in some implementations may be incorporated as a piece-wise wave propagator for which individual pieces of the solution correspond to sections of the drill string that have constant properties, such as inner or outer diameter.
  • Drill tool assemblies can be considered as slender, one-dimensional objects, and their properties can be effectively described as a function of arc length, l, and time, t. Incorporating in its entirety the methods described in greater detail in WO2009/155062, the configuration of the drill tool assembly can be uniquely defined in terms of a total axial elongation, or stretch, h(l,t), and total torsion angle, or twist, ⁇ (l,t). It may be assumed that the borehole exerts the necessary forces to keep the drill tool assembly in lateral equilibrium along its entire length.
  • the drill tool assembly When the drill tool assembly is in the borehole, it is constrained by the forces imparted to it by the borehole walls, such that its shape closely follows the trajectory of the borehole, which can be tortuous in complex borehole trajectories.
  • the dynamics of the drill tool assembly are represented by partial differential equations along with suitable constitutive relations, external forces and torques, and appropriate boundary conditions at the ends of the drill tool assembly.
  • the reference levels of downhole and surface vibration parameters identified above may be applied to the boundary conditions.
  • An exemplary flow chart 200 is presented in FIG. 3 to describe one means of reducing various embodiments of the inventive subject matter to practice.
  • the drill tool assembly description 202 , the range of measured depths, and operational RPM ranges are used to compute 204 a) the “primary period” P 1 of vibrations, and b) the “cross-compliance” X P1 of the drilling assembly at the primary period, from the rotary drive mechanism at the surface through all drilling components to the bit, as a function of measured depth MD.
  • the peak-to-peak operating parameters and periodicity 208 of quantities such as torque, WOH, WOB, and RPM may be determined using surface measurements that are incorporated into the models disclosed herein to estimate downhole operational parameters 210 .
  • corrective actions or adjustments 212 may be taken at the rig to improve drilling efficiency.
  • the measured amplitude, peak-to-peak fluctuations, periodicity, and other statistical properties of these operating parameters and the model-estimated primary period and cross-compliance are then combined to obtain a vibration amplitude ratio and, based on some reference level for the vibration amplitude ratio, a corresponding vibration severity level. Additionally, other quantities such as normalization factors and other drilling parameters may be used to provide a more comprehensive computation of the vibration amplitude ratio.
  • VAR Vibration Amplitude Ratio
  • the inventive methods may determine a vibration amplitude ratio in estimating vibration severity.
  • the vibration amplitude ratio is defined as the ratio of one or more vibration amplitudes at one or more locations. In one aspect, this could for example be a ratio of downhole fluctuations in rotary speed to the average value of the surface rotary speed. Alternatively, this could be represented as a ratio of fluctuations in surface torque to a reference value of torque vibrations estimated from a model. This estimate determines the severity level associated with torsional oscillations, or, simply, the torsional severity estimate (TSE). Other vibration amplitude ratios can be developed including those for axial vibrations, such as an axial severity estimate (ASE).
  • ASE axial severity estimate
  • WO2009/155062 contains a complete description of the governing drill string physics, this reference may be considered to be available for use with some embodiments of the methods disclosed herein.
  • the model disclosed therein makes the so-called “soft-string” approximation, i.e. it assumes that the drill string has negligible bending stiffness.
  • the use of a “stiff-string” model that includes drill string bending stiffness may also be used within the scope of the invention described herein.
  • the state vector [ ⁇ P (l), ⁇ P (l)] T represents a harmonic torsional wave along the drill tool assembly.
  • ⁇ P (l) and ⁇ P (l) are the (complex) twist and torque amplitudes of the wave mode of period P at a distance l from the bit end, respectively.
  • ⁇ ( l,t ) Re[ ⁇ P ( l ) e 2 ⁇ jt/P ].
  • a 2 ⁇ 2 transfer matrix S P (l,l′) relates the state vectors at two different positions along the drilling assembly:
  • Eq. (87) and (96) below are representative Sp matrices.
  • S(MD, 0) S ⁇ 1 (0, MD).
  • the baseline solution, frequency eigenstates, and linear response functions provided by the base model may be used with the techniques taught and claimed herein to evaluate bit bounce and stick-slip tendencies of drill tool assembly designs, which may be by means of “vibration indices” derived from these results.
  • the effective torsional compliance of the drill tool assembly at the bit position is defined as:
  • CT P bit ⁇ P bit ⁇ P bit . ( 4 )
  • the torsional compliance relates the angular displacement amplitude to the torque amplitude.
  • the resonant frequencies of the drill tool assembly have an associated period of oscillation, Pn (seconds).
  • Pn seconds
  • the first fundamental mode has a period of oscillation, P 1 (seconds).
  • the cross-compliance is defined for a particular harmonic mode with period P (seconds) as the ratio of the vibration amplitude at the bit (for instance, RPM) to the vibration amplitude (for instance, torque) at the surface (here 60/P represents the number of periods per minute):
  • the rig-to-bit transfer matrix has the simple form
  • twist and torque have the following form:
  • One practical benefit of this method is that it automatically detrends the average or slowly varying portions of both signals, i.e., it is not sensitive to the slowly varying baseline torque and RPM. It is also not necessary to separately keep track of the period P 1 . However, in some instances reliability may be somewhat compromised from noisy measurements, so the sampling rate has to be sufficiently frequent to allow a good determination of the time derivative; alternatively, the use of more sophisticated methods may be applied to obtain a smoother estimate of the derivative. Also, it may be necessary to increase the surface data acquisition recording rate to facilitate the torque derivative method described above.
  • Using a combination of several downhole vibration severity estimation methods can potentially improve the robustness of the overall method.
  • alternate means of processing surface parameter data may lead to different values for the torsional severity estimate.
  • Average values and other means of combining the results of multiple measurements may be used to seek the best estimate.
  • These different TSE estimates, from both individual and combined parameters, may be evaluated using quality factor calculations in wells for which downhole measurements are available. This calibration process will help to determine the optimal means for processing surface measurement data to assure that the torsional severity estimates have the highest quality factors possible.
  • Exemplary flow charts are presented in FIG. 4 and FIG. 5 as some examples of various embodiments for how the inventive methods may be reduced to practice.
  • the drill tool assembly description Prior to the start of drilling a section of a well, the drill tool assembly description, the range of measured depths and operational RPM ranges are used to compute a) the “primary period” P 1 of torsional/axial vibrations, and b) the “cross-compliance” X P1 of the drilling assembly at the primary period, as a function of measured depth MD.
  • These quantities are then provided to the surface monitoring system in the form of look-up tables, plots, or interpolating functions, to be used for real-time computations to monitor modal vibration severity during drilling.
  • TSEn The severity of the nth resonant torsional vibration is referred to as “TSEn.” If there is also a need to monitor forced torsional vibration severity, “normalization factors” NF can also be pre-computed as a function of RPM and MD and provided to the surface monitoring system.
  • Unstable Torsional vibration is reflective of downhole torque fluctuations from various origins and is typically associated with a dynamic instability or near-instability of the downhole drilling assembly.
  • “Unstable torsional oscillations,” commonly referred to as “stick-slip,” have a characteristic period P that is determined primarily by the drilling assembly design parameters such as material properties (steel), dimensions (length, OD, ID, relative position along the assembly), and the measured bit depth (overall length of the drilling assembly).
  • An exemplary calculation of this period can be obtained with a torsional harmonic wave mode in a drill tool assembly system with a “fixed” dynamic boundary condition at the rig end (corresponding to a constant rotary speed imposed by the rig control system) and a “free” dynamic boundary condition at the bit end (corresponding to a constant torque at the bit).
  • ⁇ rig and ⁇ bit refers to the dynamic twist and torque amplitudes, i.e. they are differences between the current values of those variables and their average, steady-state values.
  • a solution to the transfer matrix equation with these constraints exists only for specific values of the harmonic period P.
  • There exists a sequence of such modes of decreasing periods, whereby each successive mode shape in the sequence has one more “node” (position along the drilling assembly with no harmonic motion, i.e., ⁇ 0). These are referred to herein as “resonance modes” of the drilling assembly.
  • P 1 the mode with the longest period (P 1 ), which has its only node at the surface (rig) end.
  • P 1 the longest period
  • a number of search algorithms are known that can be employed to identify this period P 1 .
  • This period increases as a function of measured depth (MD) and is commonly in the range from approximately two to eight seconds for typical drilling assemblies and MD's.
  • the boundary condition at the surface is not known, it is possible to determine the effective boundary condition by measuring both torque and rotary speed and constructing the effective rig compliance from the measurements, using one of several state variable observer methods.
  • Unstable Torsional Severity When the period P is known as a function of MD, the cross-compliance at the primary period can be pre-computed for the section to be drilled. During drilling, the surface monitoring system may use the real-time MD and model results to compute TSEu as described above. Typically, the unstable torsional severity is associated with the primary resonant mode with period P 1 and is equal to the torsional severity TSE 1 evaluated at period P 1 . TSEu is also referred to herein in by the often commonly used vernacular of “unstable stick-slip” (USS), but the term TSEu is preferable as it reminds that the value is only an estimate. However, the terms are interchangeable.
  • USS unstable stick-slip
  • a second potential source of severe torsional oscillations is associated with the periodic excitation of the drilling assembly at a particular frequency.
  • the excitation occurs at or near the bit, at a multiple of the rotary speed (RPM). If this excitation period is close to one of the resonant mode periods of the drilling assembly (see above) large fluctuations may result, leading to stick-slip.
  • the cross-compliance is computed for a range of periods corresponding to the expected RPM ranges and depths. These are then converted to normalization factors using the relationship:
  • torsional severity estimation during drilling may be made using the streaming surface torque signal in the following way.
  • the torsional vibration amplitude is computed as the “peak-to-peak torque,” delta-Torque, or dTorque, and consequently may be used to estimate the torsional severity TSE 1 :
  • TSE ⁇ ⁇ 1 Downhole ⁇ ⁇ Peak ⁇ - ⁇ to ⁇ - ⁇ Peak ⁇ ⁇ RPM 2 ⁇ Surface ⁇ ⁇ RPM ⁇ ⁇ X P ⁇ ⁇ 1 ⁇ * dTorque 2 ⁇ RPM . ( 8 )
  • TSE 1 can be obtained using the concept of a reference dTorque.
  • the reference dTorque as calculated from the model cross-compliance and the surface RPM is a reference surface condition associated with full stick-slip at the bit. This quantity represents the torque fluctuation level corresponding to a condition where the bit oscillates between 0 and two times the average RPM.
  • the reference dTorque, dT 0 can be obtained for a range of rotary speeds and is obtained as:
  • TSE 1 can be obtained by identifying the reference time-derivative of the surface torque signal for the particular mode of interest:
  • TSE ⁇ ⁇ 1 ⁇ d ⁇ rig d t ⁇ ( d ⁇ d t ) ref
  • TSE 1 can be converted to any one of these alternate representations if desired.
  • a value of TSE 1 less than 1 represents RPM fluctuations at the bit that do not involve actual stopping or reversal of bit rotation, whereas a value larger than 1 corresponds to actual “sticking” or stopping of the bit during the cycle and should be a cause for concern.
  • This computation will provide a value for TSE 1 continuously, regardless of whether the dominant torsional behavior associated with the fundamental mode is present or not. If the value reported to the driller is a cause for concern, the driller can verify that unstable stick-slip is present by inspecting the torque indicator and noting that the torque fluctuations have a characteristic period close to or slightly longer than P 1 . This period is dependent on the MD and increases with increasing MD. For typical drilling operations, this period is in the range of 2-8 seconds and is easily observable. If confirmed, the driller can take corrective action as desired.
  • the surface monitoring system can be configured to display the forced torsional severity FTS instead. This is estimated by multiplying TSE 1 with the appropriate “normalization factors” NF:
  • TSEf Downhole ⁇ ⁇ Peak ⁇ - ⁇ to ⁇ - ⁇ Peak ⁇ ⁇ RPM 2 ⁇ Surface ⁇ ⁇ RPM ⁇ TSE ⁇ ⁇ 1 * NF ( 11 )
  • the surface monitoring system can display both forced and resonant vibration amplitude ratios and the driller can consider the appropriate severity level depending on the period of the dynamic torque signal.
  • Both the nth resonant torsional severity estimate, TSEn, and the forced torsional estimate, TSEf also sometimes called Forced Stick Slip (FSS)
  • TSEf also sometimes called Forced Stick Slip
  • TSEf torsional vibration amplitude ratios or torsional severity estimates
  • Other methods can be adopted to identify when these estimates can be used. For instance, if the surface monitoring system is capable of real-time spectral analysis, the torque signal can be analyzed for the prevalent period to automatically decide the type of stick-slip that is present, and the appropriate severity level can then be displayed. It is beneficial to the driller to know the type of torsional oscillations as well as the severity, since mitigation measures may be different for each type.
  • a reference surface dTorque (dT 0 ) can be obtained by calculating the cross-compliance at the stick-slip period using the drill tool assembly description and the rotary speed. This calculation is obtained based on a spectral analysis method wherein at any given time a specific frequency associated with the stick-slip period is used to extract the cross-compliance.
  • a plot of the reference surface dTorque as a function of measured depth and RPM is outlined in FIG. 6 . This plot represents an exemplary form of the dTorque as a function of these quantities.
  • reference surface dTorque also increases. In other words, there is a greater capacity to allow dTorque without encountering actual stopping of the bit, i.e., there is an increased “dTorque margin.”
  • Other alternate representations of the reference surface dTorque include descriptions in tabular form and a fitted equation that describes the reference surface dTorque per unit RPM as a function of measured depth.
  • Yet another alternate representation is to directly incorporate the cross-compliance instead of the concept of reference surface dTorque.
  • the reference surface dTorque is obtained based on the fundamental period P 1 at each Measured Depth. Thereby, the reference surface dTorque associated with forced torsional severity is incorporated to obtain more conservative reference surface dTorque values.
  • the period associated with reference torsional oscillations can be described in terms of the measured depth.
  • An exemplary chart is provided in FIG. 7 that illustrates the fundamental stick-slip period P 1 varying between 2-5 seconds at depths of 3000-9000 ft.
  • a measured torsional period at the rig that is greater than the value indicated for the specific depth, drill string, and other drilling parameters suggests that the bit is stopping for a portion of time during operation, corresponding to TSE 1 >1.
  • the ratio of the measured period to the computed period can be used to identify torsional severity level, as this ratio increases with increasing severity.
  • the measured period is expected to be substantially similar to the computed value when the torsional oscillations are less severe (TSE 1 ⁇ 1), and the time period itself does not provide a direct measure of the torsional severity beyond this information.
  • a chart of this form can be obtained either during real-time operations or pre-calculated beforehand.
  • the benefit of such a chart in real-time operations is that the precise period of interest can be obtained along with information on stoppage time and the severity of the torsional oscillations.
  • the chart can be described in a tabular form.
  • axial vibration amplitude ratio and axial severity may be accomplished using similar methods to that described above for the torsional mode.
  • axial drill string vibration models that may be used to calculate the compliance factor considered below.
  • the exemplary embodiment is the physics model described in WO 2009/155062.
  • the discussion leading up to equation (45) describes the modeling of axial vibrations that includes consideration of all the forces and moments acting on a drill string, assuming what is known as a “soft-string” model, i.e. with no bending stiffness of the string.
  • the use of a “stiff-string” model that includes drill string bending stiffness may also be used within the scope of the invention described herein.
  • the state vector [hp(l), Tp(l)] T represents a harmonic axial wave along the drill tool assembly.
  • hp(l) and Tp(l) are the (complex) stretch and tension amplitudes of the wave mode of period P at a distance l from the bit end, respectively.
  • T ( l,t ) Re[T P ( l ) e 2 ⁇ jt/P ]. (12)
  • a 2 ⁇ 2 transfer matrix S P (l,l′) relates the state vectors at two different positions along the drilling assembly:
  • Eq. (69) and (93) below are representative Sp matrices. It is generally understood (see, for example, Clayer et al. SPE 20447) that unlike torsional excitations, axial excitations typically manifest themselves as “displacement sources” and the typical dysfunction of “bit bounce” manifests itself as a dynamic fluctuation of WOB whose amplitude exceeds the average WOB. Thus, an analysis analogous to the torsional case can be done for axial vibrations. Of particular concern are harmonic axial modes in which small displacements at the bit may cause large WOB fluctuations, which can be identified through the effective axial impedance of the drill tool assembly at the bit position:
  • the measurement that is readily available at most rig systems is the weight-on-hook (WOH), so the response function of interest is the amplification factor that relates WOH fluctuations at the surface to WOB fluctuations at the bit:
  • An exemplary calculation for axial severity during drilling can be made using the streaming surface signal to compute the hookload vibration amplitude as the “peak-to-peak hookload,” delta-Hookload, dHookload, or dWOH, and consequently estimate the axial severity estimate ASE 1 :
  • ASE ⁇ ⁇ 1 Downhole ⁇ ⁇ Peak ⁇ - ⁇ to ⁇ - ⁇ Peak ⁇ ⁇ WOB 2 ⁇ Average ⁇ ⁇ WOB ⁇ ⁇ A P ⁇ ⁇ 1 ⁇ * dWOH 2 ⁇ WOB , ( 18 )
  • ASE 1 is estimated using the amplification factor A P1 evaluated at the fundamental period P 1 .
  • ASE 1 can be obtained using the concept of a reference dWOH that is associated with bit bounce.
  • the reference dWOH represents the hookload fluctuation level corresponding to a condition where the bit oscillates between 0 and two times the intended surface WOB.
  • the reference dWOH can be obtained for a range of WOB conditions and is obtained as:
  • the surface monitoring system can be configured to display the forced axial severity ASEf instead. This is estimated by multiplying ASE 1 with the appropriate “normalization factors” NF:
  • ASEf Downhole ⁇ ⁇ Peak ⁇ - ⁇ to ⁇ - ⁇ Peak ⁇ ⁇ WOB 2 ⁇ Surface ⁇ ⁇ WOH ⁇ ASE ⁇ ⁇ 1 * NF . ( 21 ) Vibration Amplitude and Time Period Estimation from Surface Signals
  • a near-real-time estimate of the amplitude of the dominant harmonic mode can be made by observing the most recent surface signature readings over a time window that is larger than the longest anticipated period but short enough to reflect near-real-time conditions.
  • an exemplary window size may be between 2 to 10 times the expected primary period P 1 at that time, to facilitate obtaining an accurate estimate of an average value as well as a peak-to-peak envelope for the surface signal.
  • a window size of 30 seconds is used.
  • the running average of the surface torque provides the average value
  • an envelope marking the maximum and minimum values of the signal function is used to identify the vibration amplitude dTorque.
  • the amplitude can be obtained by doubling the difference between the maximum and average values of the surface operating parameter within the time window. Though this method may not always be desired, in some data acquisition systems this data is currently available without modification and is approximately correct, assuming a uniform sinusoidal vibration pattern.
  • the available surface data of X average and X maximum over a suitable time window can be used to compute the “delta-X” value dX, where X refers to a quantity such as Torque, Hookload and/or RPM.
  • Another approach is to calculate the standard deviation of a time series in a rolling data buffer, wherein the new values displace the oldest values and the data window is continually refreshed.
  • One offline method which may involve only a slight time delay in the availability of the calculation results, is a phase-compensated moving average filter that can be used to compute the envelope of the surface operating parameter signal.
  • Other methods may include computing a peak-to-peak value from a real-time data stream, including methods to reduce the effect of noise, including filtering. All such methods to obtain the peak-to-peak surface operating parameter fluctuations are within the scope of this invention. In certain instances, if downhole operating parameter fluctuations are available, these can then be used to obtain improved accuracy.
  • the period of oscillation may also be estimated from the surface signals such as surface torque, hookload, and RPM.
  • the moving average is calculated over a suitably determined time window (30 seconds in this example), and whenever the signal crosses this moving average in the downward direction, a “crossing time” is estimated by linear interpolation.
  • the time interval P between successive downward crossing events defines a cycle. For each such cycle, the duration provides an estimate of the oscillation period, and the difference between the maximum and minimum values of the signal within that cycle provides an estimate of dTorque.
  • some smoothing can be performed to these estimates to make them more robust, at the cost of incremental time delay needed to identify a dysfunction.
  • smoothing can take the form of using the average or median of several successive estimates.
  • An alternate methodology is to use time-frequency analysis techniques including Fourier transforms, Wagner-Ville transforms, Hilbert Huang transforms, and wavelet transforms to identify the significant period(s) over individual time windows. Through these methods, a measure of the actual period may be obtained.
  • the estimates of significant period(s) can be used to obtain more information about the downhole scenario.
  • knowledge of the reference peak-to-peak fluctuations in surface parameters and the reference period(s) associated with the dominant harmonic modes can be combined with information about the identified periods over the specified time intervals to obtain precise information on the extent of the “stopped” time.
  • this period is observed to be greater than the estimated fundamental period or other significant periods, a measure of the stopped time (the time that the bit stops rotating during any given cycle) can be obtained by direct comparison of the estimated and measured periods.
  • the moving average is calculated over a suitably determined time window (26 seconds in this example).
  • this moving average can be calculated in a number of ways, including least squares, filtering, and spectral analysis.
  • the moving average for this example was calculated using a least squares linear fit, and is illustrated as the dashed line in FIG. 10A .
  • This moving average is then subtracted from the surface signal, leaving just the oscillatory part of the signal as depicted in FIG. 10B .
  • the Fourier transform of this signal should then be strongly peaked around the dominant oscillatory frequency and thus provides us with an estimate of the period of the dominant mode.
  • the power spectrum is filtered to remove the non-dominant noise (as illustrated in FIG.
  • Downhole data could be obtained from one or more of a downhole instrumented sub with accelerometers, force and torque sensors, and downhole measurement-while-drilling (MWD) equipment that record RPM, acceleration, WOB, and other drilling parameters.
  • MWD downhole measurement-while-drilling
  • the quantities that determine axial and/or torsional severity are then designated as VAR measured to signify a measured vibration amplitude ratio.
  • the surface estimated vibration amplitude ratios can be one or more of the torsional/axial modal vibration severity and torsional/axial forced vibration severity indices. These vibration amplitude ratios are designated as VAR estimated .
  • the quality factor may be defined in terms of conditional relations that depend on the values of the vibration amplitude ratios as follows:
  • quality factor QF describes the quality of estimation, both false negatives and false positives are lumped together.
  • An alternative is to count the quality factor associated with false positives and false negatives separately and focus on false occurrences.
  • Another alternative quality factor measurement is the goodness, which excludes false negatives/positives and counts the cases where both the measured and the estimated values are in agreement of the absence/existence of a vibration dysfunction. Cumulative statistics may be obtained and plotted in terms of histograms or other common statistical display measures. It is desirable to have a quality factor greater than 0.8 (80%) between surface estimates and downhole measurements to validate the methods described herein.
  • the driller or engineer may consider the torsional vibration type and severity under different types of boundary conditions.
  • typical torsional vibration scenarios observed under stringent RPM control where the rig end rotates substantially at the set rotary speed, the drill tool assembly can be considered as having a torsionally clamped boundary condition at the surface and a free condition at the bit.
  • An alternate scenario is to have a free boundary condition at both the bit and the surface, corresponding to torque limit control.
  • top-drive controllers such as Soft-TorqueTM and Soft-SpeedTM are used, the boundary condition at the surface is effectively somewhere in between these extreme criteria, and both Torque and RPM fluctuations may be present at the rig end.
  • FIG. 11 An exemplary graphical form of a reference condition is illustrated in FIG. 11 .
  • the observed dRPM is near zero, corresponding to the vicinity of the x-axis, and torsional severity estimate TSE 1 is given by Equation (10).
  • dTorque will be near zero and severity is determined instead from the ratio of the observed surface dRPM to the “reference dRPM” dR 0 .
  • the severity can be estimated as the ratio of distance between the origin and the current value of the surface observation,
  • the ratio of distance between the origin and the current value of the surface observation
  • the driller or engineer can consider the torsional vibration type and severity along with real-time MSE information to obtain a more comprehensive picture of downhole conditions. This may be facilitated by a display that combines all of the pertinent information advantageously.
  • An example is illustrated in FIG. 12 , whereby a two-dimensional plot 600 illustrates an evolving time-trace of the point (TSE, MSE), perhaps for a recent period of time.
  • TSE point
  • MSE multi-trace of the point
  • four regions are generally specified: Normal 610 , Stick-slip 630 , Whirl 620 , and Combined Stick-slip/Whirl 640 . While the distinction between regions may not be as strongly demarcated as indicated here, it is useful for illustrative purposes.
  • One often desired operating zone 610 is near the bottom-left corner (low MSE and low torsional severity) and a zone 640 often desired to avoid is near the top-right corner (high MSE and high torsional severity).
  • operating in the other zones may also be detrimental to tool life, ROP, footage drilled, and the costs of continued operation.
  • the zones are illustrated as having definite cut-off values, the zones in fact are often likely to blend together, transition, or extend further, such as to arbitrary cut-offs dependent on numerous other factors including formation effects, drill tool assembly dimensions, hole size, well profile and operating parameters.
  • This performance metric can be one or more of ROP, footage drilled, tool life, non-productive time associated with drilling, and formation, or some combination thereof.
  • An example of how these performance metrics can be displayed is illustrated in FIG. 13 .
  • This display can be further distilled using statistical and functional relationships of the above performance metrics, including correlations, cluster analysis, statistical time-frequency analysis, decision support systems such as neural networks, and other such methods with the objective of establishing optimized drilling parameter values such as a target range for dTorque Margin, optimal tradeoff between MSE and TSE, and even bit selection parameters such as height of depth of cut limiters to be established through field trials.
  • An exemplary method is to use the changes in performance metric, combined with changes in the severity estimate.
  • objective functions of the following forms may be used to evaluate controllable parameters in conjunction with the concept of the “dTorque Margin”:
  • the objective function here is to maximize ROP while minimizing TSE. For instance, maximizing ROP can be accomplished by increasing WOB. When the WOB is increased, the dTorque typically goes up and the TSE goes up. An objective is to ensure that there is sufficient WOB to drill efficiently without going into an undesirable operating zone. In other words, the operating conditions are maintained such that the measured dTorque is less than a specific percentage of the reference dTorque.
  • the “dTorque Margin” represents the available excess dTorque with which drilling can be carried out without concern for severe torsional dysfunctions or stick-slip.
  • the maximum value of the dTorque Margin is obtained by subtracting the surface dTorque from the reference surface dTorque, assuming that dTorque is less than the reference dTorque.
  • the use of objective functions provides a formal approach for estimation of the “available” dTorque Margin in relation to the maximum dTorque Margin. It is also important to point out that the methodology and algorithms presented in this invention are not limited to these three types of objective functions. They are applicable to and cover any form of objective function adapted to describe a relationship between drilling parameters and drilling performance measurements.
  • a base model of torsional and axial vibrations of a drill string follows directly from the patent application WO 2009/155062.
  • the zero-order and first-order terms of the perturbation expansion of the drill string equations of motion for axial and torsional vibrations are disclosed.
  • This reference includes modeling elements that include the physical effects of wellbore profile, drill string description including the effects of tool joints, inertia, friction and viscous damping, and other details necessary to provide high quality model results necessary for the present invention.
  • This is a “soft-string” model with no bending stiffness of the string.
  • the use of a “stiff-string” model that includes drill string bending stiffness may also be used within the scope of the invention described herein.
  • the present model will be disclosed in summary form, and patent application WO 2009/155062 should be referred to for additional details.
  • the present systems and methods utilize an exemplary “base model.”
  • the present methods and systems can be adapted to apply to different equations of motion and/or different base models than those presented herein. Accordingly, for the purposes of facilitating explanation of the present systems and methods, one suitable formulation of a base model is described herein and others are within the scope of the present disclosure.
  • a borehole with a particular trajectory is created by the action of a drill bit at the bottom of a drill tool assembly, consisting of drill pipe, drill collars and other elements. Drilling is achieved by applying a WOB, which results in a torque, ⁇ bit , at the bit when the drill tool assembly is rotated at an angular velocity,
  • the mechanical rotary power, ⁇ RPM ⁇ bit is supplied to the bit and is consumed during the rock cutting action.
  • the torque is provided by a drilling rig, and the WOB is typically provided by gravitational loading of the drill tool assembly elements. The application of WOB forces a portion of the drill tool assembly near the drill bit into compression.
  • the borehole centerline traverses a curve in 3-D, starting from the surface and extending out to the bottom of the hole being drilled.
  • the borehole trajectory at arc length l from the drill bit in terms of the inclination ⁇ and azimuth ⁇ as a function of measured depth (MD), global (x, y, z) and local (t, n, b) coordinates and the local borehole curvature K b can be written as:
  • t ⁇ ( l ) - sin ⁇ ( ⁇ ) ⁇ sin ⁇ ( ⁇ ) ⁇ x - sin ⁇ ( ⁇ ) ⁇ cos ⁇ ( ⁇ ) ⁇ y + cos ⁇ ( ⁇ ) ⁇ z .
  • the unit normal vector n is in the plane of local bending and perpendicular to the tangent vector t
  • the unit binormal vector b is perpendicular to both t and n.
  • the vectors x, y and z point to the East, North, and Up, respectively.
  • Drill tool assemblies can be described as a function of arc length, s, along their centerline in the unstressed state. In the stressed condition the drill tool assembly is stretched and twisted relative to the unstressed condition. The differences between the stressed and unstressed conditions are discussed further below.
  • the drill tool assembly is assumed to consist of elements attached rigidly end-to-end along a common axis of rotational symmetry, each element having a uniform cross-section along its length, free of bend and twist in its unstressed state.
  • each drill tool assembly element includes information about the material (elastic modulus, E, shear modulus, G, density, ⁇ ) and geometrical properties (area, A, moment of inertia, I, polar moment of inertia, J). This information can typically be obtained from drill tool assembly descriptions and technical specifications of the drill tool assembly components.
  • the exemplary base model considers the motion of the drill tool assembly while it is rotating at a particular bit depth (BD), WOB, and nominal rotation speed.
  • BD bit depth
  • WOB bit depth
  • nominal rotation speed The lateral displacement constraint leaves only two kinematic degrees of freedom for the drill tool assembly; stretch h and twist ⁇ .
  • the overall motion of the drill tool assembly can be described by:
  • the motions of the drill tool assembly are accompanied by internal tension, ⁇ , and torque, ⁇ , transmitted along the drill tool assembly, which can be likewise described as:
  • the drill tool assembly elements are also subject to a variety of external forces, f body , and torques, ⁇ body , per unit length that affect their motion.
  • the drilling mud shears against both the inside and the outside of the drill tool assembly, and creates forces, f mud , and torques, ⁇ mud , per unit length that resist motion. In the absence of lateral motion according to the constraints described above, no lateral forces are generated by the mud. Also, any torque that is not along the local tangent will be cancelled out by borehole torques, so we need only consider the component of torque along the tangent vector.
  • a suitable dynamic model of the mud system comprises the superposition of the dynamic effects of the mud system on the baseline solution using a model for shear stress on an infinite plane.
  • the amplitude of the shear stress acting on an infinite plane immersed in a viscous fluid and undergoing an oscillatory motion parallel to its own surface at an angular frequency w is given by:
  • ⁇ mud , ⁇ ( 1 + j ) ⁇ ⁇ ⁇ 2 ⁇ ⁇ mud ⁇ ⁇ 2 ⁇ a ⁇ , ( 41 )
  • ⁇ ⁇ is the displacement amplitude of the plane motion
  • ⁇ mud is the mud density
  • j is an imaginary number
  • ⁇ ⁇ the frequency-dependent depth of penetration
  • the penetration depth is small compared to the inner and outer radii of the element; ⁇ ⁇ ⁇ ID, OD.
  • the mud plastic viscosity term is not restricted to the Bingham model and can be easily generalized to include other rheological models, in which the viscosity term varies with RPM.
  • Eq. 41 can be used to approximate the shear stress on an annular object.
  • the borehole walls exert forces and torques that keep the drill tool assembly along the borehole trajectory.
  • the currently described model assumes that each element has continuous contact with the borehole, consistent with the soft-string approximation, and that no concentrated forces are present.
  • Other models that may be implemented within the scope of the present systems and methods may make different assumptions. For example, as discussed above, other models may use stiff-string approximations for some or all of the drill tool assembly.
  • the contact with the borehole is localized somewhere along the circumference of the element, and r c denotes the vector that connects the centerline to the contact point within the local normal plane, whose magnitude, r c , is equal to half the “torque OD” of the element.
  • a sign convention is used such that f r and f ⁇ are always positive, provided that the drill tool assembly rotates in a clockwise manner when viewed from above.
  • f n is the total borehole force in the local normal plane, with magnitude f n .
  • the dependence of the friction angle, ⁇ C , on the relative velocity of the element, ⁇ rel , with respect to the borehole can be expressed in terms of a logarithmic derivative,
  • C ⁇ ⁇ ⁇ ln ⁇ ⁇ sin ⁇ ⁇ ⁇ C ⁇ ln ⁇ ⁇ v rel v rel sin ⁇ ⁇ ⁇ C ⁇ ⁇ sin ⁇ ⁇ ⁇ C ⁇ v rel . ( 49 )
  • a negative value for C ⁇ represents a reduction of friction with increasing velocity, which may be referred to as velocity-weakening friction. Such a situation can have a significant impact on the stability of torsional vibrations and stick-slip behavior of the drill tool assembly.
  • This equation represents one manner in which a velocity-dependent damping relationship may be incorporated into the models utilized in the present systems and methods. Other equations and/or relationships may be incorporated as appropriate.
  • the baseline solution is a particular solution of the equations of motion that corresponds to smooth drilling with no vibration, at a particular bit depth, weight on bit, and specified drill tool assembly rotary speed that results in a rate of penetration.
  • the equations of motion are then linearized around this baseline solution to study harmonic deviations from this baseline solution.
  • An exemplary baseline solution is described below. As described above, a variety of equations could be used to describe the motion of the drill tool assembly considering the multitude of relationships and interactions in the borehole.
  • the baseline solution for the twist and torque can be obtained by integration, just as in the axial case.
  • the torque generated at the bit cannot be controlled independently of the WOB; the two quantities are related through bit aggressiveness.
  • the present model relates the bit torque to WOB through an empirical bit friction coefficient, ⁇ b ,
  • ⁇ bit ⁇ b ⁇ OD bit 3 ⁇ WOB . ( 58 )
  • the model uses the input parameter ⁇ b to compute the baseline solution.
  • the torque at the bit enters the baseline torque solution only additively, and does not influence the dynamic linear response of the drill tool assembly; it is there mainly to enable calibration of the model with surface measurements.
  • the model interpolates the inclination, cos ⁇ , and curvature, ⁇ b , from survey points to the midpoint of each element.
  • small motions h dyn and ⁇ dyn of an individual element may be calculated around this solution along with the associated forces (T dyn ) and torques ( ⁇ dyn ) to model the vibrations of the drill tool assembly.
  • the associated wave vector, k a , at frequency ⁇ is given by:
  • the state of the axial wave at each frequency is uniquely described by h ⁇ u and h ⁇ d .
  • the modified expression is obtained by combining equations in matrix form at two ends (locations l and l-L) of an element of length L,
  • the present model computes the transfer matrix for each element:
  • the transfer matrix Eq. (70) can be used to relate the axial vibration state anywhere along the drill tool assembly to, for example, the state at the surface end of the drill tool assembly.
  • a rig should have finite compliance against the axial and torsional modes.
  • the response of a drilling rig is dependent on the rig type and configuration and can change rapidly as the frequency of the vibration mode sweeps through a resonant mode of the rig.
  • the response of the drilling rig can be modeled and incorporated into the present systems and methods in a variety of manners, including the approach described below.
  • the drill tool assembly can be assumed to be rigidly attached to the top drive block, which can be approximated as a large point mass M rig .
  • This block is free to move up and down along the elevators, and is held in place by a number of cables that carry the hook load.
  • damping forces present which are assumed to be proportional to the velocity of the block.
  • the hoisting cable length is adjusted to achieve the desired hook load; therefore the position of the baseline axial displacement is immaterial and is not needed to compute the baseline solution. However, this length sets the equilibrium position of the spring. When the block mass moves away from the baseline position, a net force is exerted on it by the drill tool assembly and the rig.
  • This quantity measures the amount of axial movement the block mass will exhibit for a unit axial force at a particular frequency ⁇ . It is a complex-valued function whose magnitude gives the ratio of the displacement magnitude to force magnitude, and whose phase gives the phase lag between the forcing function and the resulting displacement.
  • the dynamic response of the mass-spring-dashpot system is well known and will only be described briefly.
  • Three parameters are needed to fully describe this simple dynamic rig model.
  • the block mass is typically estimated from the hook load reading with no drill tool assembly attached.
  • the spring constant can be estimated from the length, number and cross-sectional area of the hoisting cables. These two parameters define a characteristic rig frequency, ⁇ rig,a ⁇ square root over ( k rig /M rig ) ⁇ , for which the displacement of the block is 90° out of phase with the dynamic force.
  • the current model uses M rig , ⁇ rig and ⁇ rig / ⁇ crit as inputs in order to compute the dynamic response.
  • the “stiff-rig” limit can be recovered by considering the limit ⁇ rig ⁇ , where the compliance vanishes. At this limit, the rig end does not move regardless of the tension in the drill tool assembly.
  • the dynamic response of the rig is much more complicated.
  • all the information that is necessary to analyze vibration response is embedded in the compliance function, and the model framework provides an easy way to incorporate such effects. If desired, it is possible to provide the model with any compliance function, possibly obtained from acceleration and strain data from a measurement sub.
  • the effective compliance of the rig will vary with the traveling block height and the length and number of the cables between the crown block and traveling block.
  • the traveling block height varies continuously as a joint or stand is drilled down and the next section is attached to continue the drilling process.
  • the number of such cable passes may vary as the drilling load changes.
  • the derrick and rig floor is a complex structure that is likely to have multiple resonances which may have interactions with the variable natural frequency of the traveling equipment.
  • the actual dynamic motion of the drill tool assembly at a given point is given by a linear superposition of these state vectors with different amplitudes at different frequencies.
  • the main interest will be the dynamic linear response of the system to excitations at a given point along the drill tool assembly.
  • the response of the system to multiple excitations can likewise be analyzed using the superposition principle.
  • the effective drill tool assembly compliance at the bit can be defined as:
  • the methodology used for obtaining the expressions for torsional waves is similar to that described above for axial waves.
  • the methodology used for obtaining these equations and expressions is included within the scope of the present disclosure regardless of the selected starting equations, boundary conditions, or other factors that may vary from the implementations described herein.
  • the dynamic torque associated with the borehole forces is computed using the lateral motion constraint and the Coulomb criterion.
  • the present model currently decouples these effects and explores axial and torsional modes independently. The decoupling is accomplished by setting the tension, T dyn , to zero while analyzing torsional modes.
  • the velocity-dependent damping relationships incorporated into the models of the present systems and methods provide models that are more reliable and more accurate than prior models. More specifically, it has been observed that the mud damping effect increases with increasing velocity whereas the borehole damping effect actually decreases with increasing velocity. Accordingly, in some implementations, models that incorporate both mud effects and borehole effects may be more accurate than models that neglect these effects. While the mud effects and borehole effects may be relatively small, the appropriate modeling of these effects will increase the model accuracy to enable drilling at optimized conditions.
  • the torque amplitude is given by:
  • the transfer matrix formalism can be used to relate twist and torque amplitudes at the two ends of an element:
  • the rest of the torsional formulation precisely follows the axial case, with the appropriate substitution of variables and parameters.
  • the torsional compliance at the surface is defined similarly, using appropriate torsional spring, damping and inertial parameters.
  • the model can accommodate special elements, in its general framework. In general, these can be accommodated as long as expressions relating the baseline solution across the two ends, as well as its associated dynamic transfer matrix, can be described.
  • Many tubular components of the drill tool assembly do not have a uniform cross-sectional profile along their length. They tend to be bulkier near the ends (tool joints) where connections are made, and slimmer in the middle. Heavy weight drill pipe and other non-standard drill pipe can also have reinforced sections where the cross-sectional profile is different from the rest of the pipe. Many drill pipes also have tapered cross sections that connect the body of the pipe to the tool joints at the ends, rather than a piecewise constant cross-sectional profile. To construct a drill tool assembly, many nearly identical copies of such tubular components are connected end-to-end to create a structure with many variations in cross-section along its length. Representing each part with a different cross-section as a separate element is tedious and computationally costly.
  • the torsional baseline solution can be obtained by replacing the torque outer diameter, r c , and the inverse of the polar moment of inertia 1/J, by their averaged versions.
  • the most significant effect of using drill tool assembly components with a non-uniform cross-section is to change the wave vectors associated with axial and torsional waves at a given frequency by a constant shape factor.
  • the velocities of axial and torsional waves along this section of the drill tool assembly are reduced by s A and s J , respectively.
  • This causes an associated shift of resonant frequencies of the drill tool assembly to lower values, which can be important if the model is used to identify RPM “sweet spots”.
  • the costs of drilling operations makes even minor improvements in predictions and corresponding operations efficiencies valuable.
  • the tool joints may cause a downward shift of resonant frequencies of up to about 10%, compared to a drill pipe of uniform cross-section. This can be significant depending on the application, and may be included in an exemplary embodiment of the invention.
  • the baseline solution, frequency eigenstates, and linear response functions provided by the base model may be used to evaluate downhole vibration attributes that include but are not limited to bit bounce and stick-slip tendencies of drill tool assembly designs, which may be by means of compliances derived from these results. More specifically, downhole vibration attributes for the drill tool assembly may include but are not limited to bit disengagement index, ROP limit state index, bit bounce compliance index, bit chatter index, relative bit chatter index, stick-slip tendency index, bit torsional aggressiveness index, forced torsional vibration index, relative forced torsional vibration index, axial strain energy index, torsional strain energy index, and combinations thereof. Without restricting the scope of the claimed invention, a few examples are presented below.
  • a downhole vibration attributed may be determined by the effective compliance (axial and torsional) of the drill tool assembly:
  • the axial compliance provides the relationship between the axial displacement and tension amplitude at a particular frequency.
  • the torsional compliance relates the angular displacement amplitude to the torque amplitude.
  • the compliance is a complex function of ⁇ and has information on both the relative magnitude and phase of the oscillations.
  • Compliance functions defined at the bit can be referenced to surface parameter measurements using the bit-to-surface transfer functions described in (93) and (96). In the following discussion, certain relationships are discussed which can thereby be referenced to surface measurements.
  • the indices below are exemplary Vibration Amplitude Ratios which may be translated to the surface using the methods taught above, with corresponding reference values translated to reference values of surface parameters for comparison with surface measurements to obtain the desired real-time vibration severity estimates to improve drilling performance.
  • PDC bits the number of blades is likely to be an important harmonic node.
  • the origin of the displacement excitation is the heterogeneity in the rock, such as hard nodules or streaks, or transitions between different formations. While passing over these hard streaks, the drill bit is pushed up by the harder formation. If the additional axial force that is generated by the drill tool assembly response to this motion exceeds the WOB, the resulting oscillations in WOB can cause the bit to lose contact with the bottom hole. The situation is similar to the case when a car with a stiff suspension gets airborne after driving over a speed bump.
  • the effective spring constant of the drill tool assembly that generates the restoring force is given by:
  • h n ⁇ ⁇ ⁇ RPM ⁇ ( 0 ) a ⁇ PPC ; PPC ⁇ 2 ⁇ ⁇ ⁇ ROP n ⁇ ⁇ ⁇ RPM . ( 100 )
  • the proportionality constant, a, between the PPC and the imposed displacement amplitude can be adjusted from 0 to 1 to indicate rock heterogeneity, with 0 corresponding to a completely homogeneous rock and 1 corresponding to the presence of very hard stringers in a soft rock.
  • a bit bounce index can then be defined by the ratio of the dynamic axial force to the average WOB. Setting the proportionality constant, a, to one corresponds to a worst-case scenario:
  • the bit would completely disengage from the rock for part of the cycle if this ratio exceeds one, so the design goal would be to minimize this index; keeping it small compared to one.
  • the index is only relevant when the real part of the compliance is negative, that is, when the drill tool assembly actually pushes back.
  • the first ratio in this expression depends on the bit and formation characteristics, and this can be obtained from drill-off tests at the relevant rotational speeds.
  • the vibrational performance of an already-run drill tool assembly design can be hindcast using ROP and WOB data in the drilling log.
  • pre-drill ROP “limit state” estimate associated with a bit bounce index of one:
  • a contour plot of this quantity will indicate, for a given set of drilling conditions, the ROP beyond which bit bounce may become prevalent and the design goal would be to maximize the ROP within an operating window without inducing excessive or undesirable bit bounce.
  • a more conservative index can be used by replacing the real part with the magnitude and disregarding the phase.
  • the discussion above illustrates several available indices that can be developed from the relationships within the borehole. Other suitable indices may be developed applying the systems and methods of the present disclosure and are within the scope of the present disclosure.
  • Regenerative chatter is a self-excited vibration, where the interaction between the dynamic response of the drill tool assembly and the bit-rock interaction can cause a bottom hole pattern whose amplitude grows with time. This is a well-known and studied phenomenon in machining, metal cutting and milling, and is referred to as “chatter theory”. In comparison to the earlier discussion, this type of instability can occur in completely homogeneous rock and is more directly tied to the drill tool assembly design.
  • PPC penetration per cycle
  • While torsional vibration also referred to as stick-slip, can be caused or influenced by a number of factors within the borehole, the interaction between the bit and the formation is an important factor.
  • bit-induced stick-slip is that it arises as an instability due to the dependence of bit aggressiveness (Torque/WOB ratio) on RPM.
  • Most bits exhibit reduced aggressiveness at higher RPMs.
  • WOB the torque generated by the bit actually decreases as the bit speeds up, resulting in RPM fluctuations that grow in time. What prevents this from happening at all times is the dynamic damping of torsional motion along the drill tool assembly.
  • active control such as Soft TorqueTM.
  • the presently-described model locates the first resonance and uses it to assess stick-slip performance.
  • Other suitable models used to develop indices may consider other resonances.
  • a suitable stick-slip tendency index can be constructed as:
  • the factor multiplying the overall damping coefficient is chosen to non-dimensionalize the index by means of a characteristic torque (rig torque) and angular displacement (encountered at full stick-slip conditions). Another reasonable choice for a characteristic torque would be torque at the bit; there are also other characteristic frequencies such as the stick-slip frequency. Accordingly, the index presented here is merely exemplary of the methodology within the scope of the present disclosure. Other index formulations may be utilized based on the teachings herein and are within the scope of the present invention. The design goal of a drill tool assembly configuration design and/or a drilling operation design would be to primarily avoid regions where this index is negative, and then to minimize any positive values within the operating window.
  • bit aggressiveness requires information about how the bit torque depends on RPM.
  • the exemplary embodiment uses a functional form for the bit aggressiveness as follows:
  • D b ⁇ WOB ⁇ d + ⁇ s - ⁇ d 1 + ( ⁇ RPM / ⁇ XO ) , ( 113 )
  • D b is the bit diameter.
  • Other implementations may utilize other relationships to describe how the bit torque depends on RPM. According to the present implementation, as the RPM is increased, the bit aggressiveness goes down from its “static” value ⁇ s at low RPMs towards its “dynamic” value ⁇ d at high RPMs, with a characteristic crossover RPM associated with angular velocity ⁇ XO . Then,
  • a relative index can be used for the purposes of side-by-side comparison of drill tool assembly designs by assuming suitable default values, such as 0.3 for bit aggressiveness and no velocity weakening. This index will not allow determination of when stick-slip will occur, but will provide a relative comparison between different drill tool assembly designs meant for the same bit, with the better designs having a lower index:
  • the drill bit is assumed to act as a source of torque oscillations with a frequency that matches the rotary speed and its harmonics.
  • severe torsional oscillations can be induced due to the large effective compliance of the drill tool assembly, i.e., a small torque oscillation can result in a large variation in the rotary speed of the bit.
  • the effective torsional compliance at the bit, taking into consideration drill string and bit damping is given by,
  • C eff ⁇ ( ⁇ ) [ 1 C bit * ⁇ ( ⁇ ) + 1 C ⁇ , bit ⁇ ( ⁇ ) ] - 1 ( 116 )
  • C* bit ( ⁇ ) 1/j ⁇ bit .
  • the * is used to indicate that the term is not a true compliance and only includes the velocity weakening term associated with the bit aggressiveness.
  • index is normalized such that it reflects the ratio of a characteristic torque (chosen here as the torque at the surface) to the excitation torque amplitude needed to achieve full stick-slip at the bit. Another reasonable choice for a characteristic torque would be torque at the bit.
  • characteristic frequencies that can be considered, another example is disclosed below. Accordingly, the index presented here is merely exemplary of the methodology within the scope of the present disclosure. Other index formulations may be utilized based on the teachings herein and are within the scope of the present invention. The design goal would be to minimize the index within the operating window.
  • the amount of stored elastic energy in the drill tool assembly resulting from dynamic conditions can be an indicator of excessive motion that can lead to drill tool assembly damage, wear of pipe and casing, and perhaps even borehole breakouts and other poor hole conditions.
  • the amount of stored elastic energy in the drill tool assembly may be written in integral form as:
  • the hole curvature can be considered to be pre-determined and not part of the dynamics problem
  • the first two terms in the integrand, the dynamic axial strain energy and torsional strain energy respectively may be used as, or considered in, additional vibration indices. Better performance would generally be associated with lower index values calculated as follows:
  • the particular solutions used in computing the indices above can be the baseline solution, the dynamic part of the linear response functions at a relevant frequency (a harmonic of the RPM, or a resonant frequency in the case of chatter or stick-slip), or a superposition of the two.
  • FIG. 14 illustrates a collected presentation of time related data 700 , wherein the top panel 710 reflects a portion of the rotary speed data, whereby the smooth line is surface data and the cross-hatched region represents the downhole data.
  • a zoom-in to the data (not shown) reveals that the prevalent behavior is “unstable torsional oscillation,” and the RPM variations occur at a period close to the computed primary period P 1 .
  • the middle panel 720 illustrates the torque signal observed at the rig (jagged line) and downhole (smoother line). Large torque fluctuations with the same period are evident whenever stick-slip severity is large, even though the torque at the bit is relatively steady, consistent with the postulated boundary conditions.
  • the bottom panel 730 reflects a comparison of torsional severity (here reported as the ratio of RPM fluctuation amplitude and average RPM, in percent) obtained directly from the downhole data and estimated from the rig torque signal using the method disclosed herein.
  • the two curves track each other very well, except when the top drive RPM is changed to a new value, which is expected.
  • the ROP and MSE data displayed on the rig during this interval.
  • the ROP and MSE signals do not correlate well with the torsional severity.
  • One exception is the interval around 3700 seconds where high values of both MSE and torsional severity are seen. Further analysis of the downhole data suggests coexisting stick-slip and whirl in this interval.
  • the ability to monitor both MSE and TSE 1 can provide more insight on downhole behavior, compared to either signal on its own.
  • FIG. 15 illustrates one method of how the inventive method may be practiced.
  • the reference surface dTorque is estimated by using the surface RPM and pre-calculating the cross-compliance using the drill tool assembly description. Additionally, the surface dTorque is calculated from the surface Torque data. In this particular instance, data was available at one second intervals. This ensured that the minimum Nyquist criterion associated with the fundamental period was met.
  • the two sets of curves (reference surface dTorque and measured surface dTorque) are illustrated in FIG. 15 . An alarm sequence is then developed based on consideration of safe operating zones and the reference operating zones.
  • the measured surface dTorque is divided into three distinct segments: (a) less than 60% of reference dTorque, (b) between 60% and 80% of reference dTorque, and (c) greater than 80% of reference dTorque.
  • a less than 60% of reference dTorque
  • b between 60% and 80% of reference dTorque
  • c greater than 80% of reference dTorque.
  • FIG. 15 also illustrates a segment indicating “dTorque margin,” which corresponds to the difference between the reference surface dTorque and the measured surface dTorque.
  • This excess dTorque suggests that the bit can be drilled more aggressively at higher WOB's with greater depth of cut.
  • the rotary speeds could be lowered while continuing to operate at some level of torsional oscillations if deemed appropriate to mitigate other vibration modes.
  • the ability to monitor dTorque in conjunction with the reference dTorque can provide more insight on what is happening downhole with suitable mitigation options to drill more efficiently. This monitoring and adjustment of the drilling parameters may be performed in real time while the well is being drilled.
  • the dTorque and reference dTorque values may be combined to obtain the TSE.
  • the results may be displayed such as in the set of graphs 800 illustrated in FIG. 16 , wherein TSE is compared with measured downhole torsional severity.
  • the downhole measurements are obtained by computing a ratio of the maximum fluctuations in rotary speed to the average value of the rotary speed. It is observed that quantitative and qualitative values match well throughout the depth range of interest, which is comprised of about 1700 data points.
  • the quality factor (QF) described in Eq. (23) is then used to compute the accuracy of the estimate. This detail is displayed as the quality factor curve in the third chart in FIG. 16 .
  • a histogram may be used to visually demonstrate the distribution of the measured torsional severity 810 of the downhole vibrations at the bit, as seen in FIG. 17 .
  • This chart demonstrates that although most of the time the bit was in less than 25% stick-slip, there were occasions when the bit was stuck for a more significant period of time.
  • the bit may momentarily be in full stick-slip. When the momentarily stuck bit becomes free it can accelerate to a value of more than two times the average surface rotary speed. When this occurs, the TSE curve 820 may reflect a TSE value that is relatively close to, meets, or even exceeds a value of one.
  • the distribution of the torsional severity estimate TSE 820 (that was calculated or otherwise determined from the surface data using the drill string model described herein) is illustrated as a histogram chart in FIG. 18( a ).
  • the Quality Factor (QF) 830 in FIG. 16 was calculated and presented to compare the measured 810 and calculated 820 severity data.
  • This QF distribution is provided as a histogram in FIG. 18B .
  • the chart in FIG. 18( b ) is peaked towards a quality factor of 100%, as desired.
  • the torsional vibration severity was also estimated using a simple model that considers only the length and static torsional stiffness of the drill sting component in the drill tool assembly. This model does not consider certain drill string physics that are present and as such provides a less reliable determination of TSE than the methods such as disclosed herein.
  • the results of this analysis are illustrated in FIG. 19 .
  • FIG. 19( a ) somewhat resembles the measured TSE of FIGS. 17 and 18( a ), some divergence is notable.
  • the QF was calculated for this estimate, and the distribution is presented in FIG. 19( b ).
  • Comparison of chart FIG. 19( b ) with FIG. 18( b ) demonstrates a significant reduction in the quality of the downhole torsional vibration severity estimate TSE from the same surface data.
  • TSE may provide some indication of the relative amounts of stick-slip that were present in the drilling operations of each of Well A and Well B. This valuable information can be used in a continuous optimization process, or “relentless re-engineering” effort to combine this information with other data such as: average ROP, bit dull characteristics, Mechanical Specific Energy (MSE), number of bit runs required to drill the section, and other vibration and drilling performance indicators known to those skilled in the art.
  • MSE Mechanical Specific Energy
  • the estimated downhole vibration amplitude (e.g., torsional, axial, etc.), when divided by the reference downhole vibration amplitude, provides a numerical estimate of how close the drilling operation is to the reference state. However, as discussed above, it may be more convenient to provide instead an alarm level associated with the estimate. For instance, low levels of estimated vibration amplitude may yield a green light, high levels a red light, and intermediate levels a yellow light.
  • Such a discrete classification scheme may be validated using downhole data with a table similar to that in FIG. 21 .
  • a green light is associated with measured surface dTorques of less than 70% of the reference dTorque; a red light is associated with measured surface dTorques of more than 100% of the reference dTorque; and a yellow light is associated with all intermediate measured surface dTorques.
  • the estimated value e of the downhole vibration amplitude severity may be compared to the measured value m at any point in time.
  • Each cell in the table gives the fraction of the time periods during the drilling operation in which e lies in the range indicated in the leftmost column and m lies in the range indicated in the topmost row.
  • the row sums in the rightmost column give the total fraction of the time periods that the different light colors were displayed, and the column sums in the bottommost row give the total fraction of the time periods that amplitudes corresponding to the different light colors were measured downhole.
  • the “rate of false negatives” is the fraction of the time in which e indicated a green light but the downhole measurement warranted a red light.
  • the “rate of false positives” is the fraction of the time in which e indicated a red light but the downhole measurement warranted a green light.
  • the “total badness” is then just the sum of these two rates, and is a measure of how often the estimate was most consequentially wrong.
  • the “full stick-slip prediction accuracy” is the fraction of the time spent in red light conditions downhole during which e correctly indicated a red light.
  • the “stick-slip warning accuracy” is the fraction of the time spent in yellow or red light conditions downhole during which e indicated either a yellow or a red light.
  • the method disclosed herein teaches and enables drilling operations performance engineering methods that were previously not available using previously available methods that relied only upon surface data measurements to estimate or project downhole responses.
  • the presently claimed methodology provides enabling tools and technology to optimize the wellbore drilling process.
  • the present inventive subject matter may include:
  • a method to estimate severity of downhole vibration for a wellbore drill tool assembly comprising the steps:
  • step c Determining a surface parameter vibration attribute derived from at least one surface measurement or observation obtained in a drilling operation, the determined surface parameter vibration attribute corresponding to the identified surface drilling parameter (step c);
  • the identified dataset comprises one or more of selected drill tool assembly design parameters, wellbore dimensions, measured depth (MD), projected drilling operation parameters, wellbore survey data, and wellbore fluid properties.
  • step b is selected as a function of one or more of downhole drill tool assembly rotational velocity, downhole axial velocity or acceleration, downhole axial load, downhole torsional moment, and combinations thereof.
  • vibration relates to vibration of one or more components of the drill tool assembly and comprises one or more of torsional vibration, axial vibration, lateral vibration, and combinations thereof.
  • selecting a reference level of downhole vibration amplitude comprises selecting a downhole condition for the drill tool assembly for which the rotary velocity is momentarily zero.
  • selecting a reference level of downhole vibration amplitude comprises selecting a downhole condition where a weight on bit (WOB) parameter is momentarily zero.
  • selecting the reference level of downhole vibration amplitude comprises selecting an undesirable downhole condition.
  • identifying the surface drilling parameter and calculating a reference surface vibration attribute includes calculating a reference value for one or more of a surface indicated torque, a surface indicated hook load, a surface indicated rotational velocity of the drill string, a surface indicated bit penetration rate, a surface indicated axial acceleration, and combinations thereof.
  • step c includes determining one or more of vibration amplitude, period, primary period, standard deviation, statistical measure, time derivative, slew rate, zero crossings, Fourier amplitude, state observer estimate, other mode observer estimate, resonance, cross compliance, and combinations thereof.
  • determining the surface parameter vibration attribute includes determining one or more of a surface torque, a surface hook load, surface rotational velocity of the drill string, a surface measured bit penetration rate, a surface measured weight on bit, a surface axial acceleration, and combinations thereof.
  • step d includes calculating a reference value for one or more of a surface indicated torque, a surface indicated hook load, a surface indicated rotational velocity of the drill string, a surface indicated bit penetration rate, a surface indicated axial acceleration, and combinations thereof.
  • step d comprises using one or more of vibration amplitude, period, primary period, standard deviation, statistical measure, time derivative, slew rate, zero crossings, Fourier amplitude, state observer estimate, other mode observer estimate, resonance, cross compliance, and combinations thereof.
  • step e further comprises:
  • step b Determining one or more ratios of: the selected reference level of downhole vibration amplitude for the drill tool assembly (step b) to the calculated reference surface vibration attribute (from this step c);
  • Estimating the downhole vibration severity indicator by evaluating the determined surface parameter vibration attribute (step d) with respect to one or more of the determined ratios.
  • step e further comprises:
  • Calculating a reference surface vibration attribute comprises calculating a rate of change with respect to time of a surface parameter for a reference level of a downhole vibration attribute;
  • step d Determining the rate of change with respect to time of the surface parameter (step d) from at least one measurement or observation obtained in a drilling operation;
  • Estimating a downhole vibration severity indicator (step e) by evaluating the determined surface parameter rate of change (step d) with respect to the calculated reference level of the rate of change of the surface parameter (step c).
  • step e further comprises:
  • Step c Calculating a reference surface vibration attribute (step c) including determining one or more characteristic periods of vibration of the drill tool assembly;
  • step d Determining the surface parameter vibration attribute (step d) derived from at least one surface measurement or observation obtained in a drilling operation, including determining a dominant period from one or more surface parameters;
  • Estimating a downhole vibration severity indicator by evaluating the determined one or more characteristic periods and the calculated reference dominant period.
  • a method to estimate severity of downhole vibration for a wellbore drill tool assembly comprising the steps:
  • Identifying a dataset comprising (i) parameters for a selected drill tool assembly comprising a drill bit, (ii) selected wellbore dimensions, and (iii) selected measured depth (MD);
  • step c Determining a surface parameter vibration attribute value obtained in a drilling operation, the determined surface parameter vibration attribute value corresponding to the identified selected surface drilling parameter (step c);
  • step of estimating a downhole vibration severity further comprises an approximation model based upon a first order perturbation model that considers the wellbore profile, drill string dimensions, drill string inertial properties, fluid damping, borehole friction, tool joint effects, and appropriate boundary conditions that represent vibrational states of interest.
  • estimating downhole vibration severity comprises determining an estimate for at least one of downhole RPM fluctuation, a stick slip index, weight on bit fluctuation, bit bounce, drill string whirl, and combinations thereof.
  • step b) further comprises:
  • step e Providing a relative or discrete indication of the estimated downhole vibration severity of step e that reflects a drilling operation parameter that is outside of an acceptable range for such drilling operation parameter.
  • estimating downhole vibration severity further comprises determining an estimate for mechanical specific energy.
  • FSSNF forced stick slip normalization factor
  • step d is performed substantially during drilling operations and is used to monitor or reduce downhole vibration severity.
  • the determined surface parameter vibration attribute includes surface torque that comprises a peak-to-peak torque (TPP) variation for a selected unit of time.
  • TPP peak-to-peak torque
  • the estimated downhole vibration severity indicator includes at least one of unstable stick slip (USS) and bit bounce is determined from a surface parameter vibration attribute derived during drilling operations.
  • USS unstable stick slip
  • the estimated downhole vibration severity indicator includes at least one of unstable stick slip (USS) and bit bounce and is determined from a projected surface parameter vibration attribute derived prior to drilling operations.
  • USS unstable stick slip
  • MSE mechanical specific energy
  • a method to estimate severity of downhole vibration for a drill tool assembly comprising the steps:
  • step b Identifying one or more ratios of: the selected reference level of downhole vibration amplitude for the drill tool assembly (step b) to a calculated reference surface vibration attribute;
  • step c Determining a surface parameter vibration attribute derived from at least one surface measurement or observation obtained in a drilling operation, the determined surface parameter vibration attribute corresponding to the identified surface drilling parameter (step c);
  • step d Estimating the downhole vibration severity indicator by evaluating the determined surface parameter vibration attribute (step d) with respect to one or more of the identified ratios (step c).
  • a method to estimate severity of downhole vibration for a wellbore drill tool assembly comprising the steps:
  • step b Identifying one or more ratios of: the selected reference level of downhole vibration amplitude for the drill tool assembly (step b) to a rate of change associated with a selected reference surface vibration attribute;
  • step d Estimating the downhole vibration severity indicator by evaluating the determined surface parameter vibration attribute (step d) with respect to one or more of the identified ratios (step c).
  • a method to estimate severity of downhole vibration for a wellbore drill tool assembly comprising:
  • the undesirable downhole condition includes one or more of: full stick-slip of the bit, bit axial disengagement from the formation, or momentarily exceeding one or more design or operating limits anywhere along the drill tool assembly, such as the make-up or twist-off torque of a connection, a bucking limit, or a tensile or torsional strength of a component of the drill tool assembly.

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